interference of sound waves experiment

14.4 Sound Interference and Resonance

Section learning objectives.

By the end of this section, you will be able to do the following:

Describe resonance and beats
Define fundamental frequency and harmonic series
Contrast an open-pipe and closed-pipe resonator
Solve problems involving harmonic series and beat frequency

Teacher Support

The learning objectives in this section will help your students master the following standards:

(D) investigate behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Sound Waves, as well as the following standards:

Section Key Terms

beat	beat frequency	damping	fundamental	harmonics
natural frequency	overtones	resonance	resonate

[BL] Before the start of this section, it would be useful to review the properties of sound waves and how they are related to each other, standing waves, superposition and interference of waves.

Resonance and Beats

Sit in front of a piano sometime and sing a loud brief note at it while pushing down on the sustain pedal. It will sing the same note back at you—the strings that have the same frequencies as your voice, are resonating in response to the forces from the sound waves that you sent to them. This is a good example of the fact that objects—in this case, piano strings—can be forced to oscillate but oscillate best at their natural frequency.

A driving force (such as your voice in the example) puts energy into a system at a certain frequency, which is not necessarily the same as the natural frequency of the system. Over time the energy dissipates, and the amplitude gradually reduces to zero- this is called damping . The natural frequency is the frequency at which a system would oscillate if there were no driving and no damping force. The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance , and a system being driven at its natural frequency is said to resonate .

Most of us have played with toys where an object bobs up and down on an elastic band, something like the paddle ball suspended from a finger in Figure 14.18 . At first you hold your finger steady, and the ball bounces up and down with a small amount of damping. If you move your finger up and down slowly, the ball will follow along without bouncing much on its own. As you increase the frequency at which you move your finger up and down, the ball will respond by oscillating with increasing amplitude. When you drive the ball at its natural frequency, the ball’s oscillations increase in amplitude with each oscillation for as long as you drive it. As the driving frequency gets progressively higher than the resonant or natural frequency, the amplitude of the oscillations becomes smaller, until the oscillations nearly disappear and your finger simply moves up and down with little effect on the ball.

Another example is that when you tune a radio, you adjust its resonant frequency so that it oscillates only at the desired station’s broadcast (driving) frequency. Also, a child on a swing is driven (pushed) by a parent at the swing’s natural frequency to reach the maximum amplitude (height). In all of these cases, the efficiency of energy transfer from the driving force into the oscillator is best at resonance.

[BL] [OL] [AL] Tuning forks and pipes may be used to demonstrate the concept of resonance. Use any pipe or tube closed at one end. Fix it so that it stands upright with the open end on top. Choose a tuning fork and strike it to make it vibrate. Place it near the mouth of the pipe and hear the sound. Now fill the pipe with some water and repeat. The changing water level changes the length of the resonating air column. Continue doing this. When a certain length is obtained, the sound of the tuning fork will resonate through the column.

All sound resonances are due to constructive and destructive interference. Only the resonant frequencies interfere constructively to form standing waves, while others interfere destructively and are absent. From the toot made by blowing over a bottle to the recognizability of a great singer’s voice, resonance and standing waves play a vital role in sound.

Interference happens to all types of waves, including sound waves. In fact, one way to support that something is a wave is to observe interference effects. Figure 14.19 shows a set of headphones that employs a clever use of sound interference to cancel noise. To get destructive interference, a fast electronic analysis is performed, and a second sound is introduced with its maxima and minima exactly reversed from the incoming noise.

In addition to resonance, superposition of waves can also create beats. Beats are produced by the superposition of two waves with slightly different frequencies but the same amplitude. The waves alternate in time between constructive interference and destructive interference, giving the resultant wave an amplitude that varies over time. (See the resultant wave in Figure 14.20 ).

This wave fluctuates in amplitude, or beats, with a frequency called the beat frequency . The equation for beat frequency is

where f 1 and f 2 are the frequencies of the two original waves. If the two frequencies of sound waves are similar, then what we hear is an average frequency that gets louder and softer at the beat frequency.

Tips For Success

Don’t confuse the beat frequency with the regular frequency of a wave resulting from superposition. While the beat frequency is given by the formula above, and describes the frequency of the beats, the actual frequency of the wave resulting from superposition is the average of the frequencies of the two original waves.

Virtual Physics

Wave interference.

For this activity, switch to the Sound tab. Turn on the Sound option, and experiment with changing the frequency and amplitude, and adding in a second speaker and a barrier.

The amplitude decreases over time. This phenomenon is called damping. It is caused by the dissipation of energy.
The amplitude increases over time. This phenomenon is called feedback. It is caused by the gathering of energy.
The amplitude oscillates over time. This phenomenon is called echoing. It is caused by fluctuations in energy.

Fundamental Frequency and Harmonics

Suppose we hold a tuning fork near the end of a tube that is closed at the other end, as shown in Figure 14.21 , Figure 14.22 , and Figure 14.23 . If the tuning fork has just the right frequency, the air column in the tube resonates loudly, but at most frequencies it vibrates very little. This means that the air column has only certain natural frequencies. The figures show how a resonance at the lowest of these natural frequencies is formed. A disturbance travels down the tube at the speed of sound and bounces off the closed end. If the tube is just the right length, the reflected sound arrives back at the tuning fork exactly half a cycle later, and it interferes constructively with the continuing sound produced by the tuning fork. The incoming and reflected sounds form a standing wave in the tube as shown.

The standing wave formed in the tube has its maximum air displacement (an antinode ) at the open end, and no displacement (a node ) at the closed end. Recall from the last chapter on waves that motion is unconstrained at the antinode, and halted at the node. The distance from a node to an antinode is one-fourth of a wavelength, and this equals the length of the tube; therefore, λ = 4 L λ = 4 L . This same resonance can be produced by a vibration introduced at or near the closed end of the tube, as shown in Figure 14.24 .

Since maximum air displacements are possible at the open end and none at the closed end, there are other, shorter wavelengths that can resonate in the tube see Figure 14.25 ). Here the standing wave has three-fourths of its wavelength in the tube, or L = ( 3 / 4 ) λ ′ L = ( 3 / 4 ) λ ′ , so that λ ′ = 4 L / 3 λ ′ = 4 L / 3 . There is a whole series of shorter-wavelength and higher-frequency sounds that resonate in the tube.

We use specific terms for the resonances in any system. The lowest resonant frequency is called the fundamental , while all higher resonant frequencies are called overtones . All resonant frequencies are multiples of the fundamental, and are called harmonics . The fundamental is the first harmonic, the first overtone is the second harmonic, and so on. Figure 14.26 shows the fundamental and the first three overtones (the first four harmonics) in a tube closed at one end.

The fundamental and overtones can be present at the same time in a variety of combinations. For example, the note middle C on a trumpet sounds very different from middle C on a clarinet, even though both instruments are basically modified versions of a tube closed at one end. The fundamental frequency is the same (and usually the most intense), but the overtones and their mix of intensities are different. This mix is what gives musical instruments (and human voices) their distinctive characteristics, whether they have air columns, strings, or drumheads. In fact, much of our speech is determined by shaping the cavity formed by the throat and mouth and positioning the tongue to adjust the fundamental and combination of overtones.

Open-Pipe and Closed-Pipe Resonators

The resonant frequencies of a tube closed at one end (known as a closed-pipe resonator ) are f n = n v 4 L , n = 1 , 3 , 5... , f n = n v 4 L , n = 1 , 3 , 5... ,

where f 1 is the fundamental, f 3 is the first overtone, and so on. Note that the resonant frequencies depend on the speed of sound v and on the length of the tube L .

Another type of tube is one that is open at both ends (known as an open-pipe resonator ). Examples are some organ pipes, flutes, and oboes. The air columns in tubes open at both ends have maximum air displacements at both ends. (See Figure 14.27 ). Standing waves form as shown.

The resonant frequencies of an open-pipe resonator are

f n = n v 2 L , n = 1 , 2 , 3..., f n = n v 2 L , n = 1 , 2 , 3...,

where f 1 is the fundamental, f 2 is the first overtone, f 3 is the second overtone, and so on. Note that a tube open at both ends has a fundamental frequency twice what it would have if closed at one end. It also has a different spectrum of overtones than a tube closed at one end. So if you had two tubes with the same fundamental frequency but one was open at both ends and the other was closed at one end, they would sound different when played because they have different overtones.

Middle C, for example, would sound richer played on an open tube since it has more overtones. An open-pipe resonator has more overtones than a closed-pipe resonator because it has even multiples of the fundamental as well as odd, whereas a closed tube has only odd multiples.

In this section we have covered resonance and standing waves for wind instruments, but vibrating strings on stringed instruments also resonate and have fundamentals and overtones similar to those for wind instruments.

[BL] [OL] [AL] Other instruments also use air resonance in different ways to amplify sound. For instance, a violin and a guitar both have sounding boxes but with different shapes, resulting in different overtone structures. The vibrating string creates a sound that resonates in the sounding box, greatly amplifying the sound and creating overtones that give the instrument its characteristic flavor. The more complex the shape of the sounding box, the greater its ability to resonate over a wide range of frequencies. The type and thickness of wood or other materials used to make the sounding box also affects the quality of sound. Ask students to give more examples of how different musical instruments use the phenomenon of resonance.

Solving Problems Involving Harmonic Series and Beat Frequency

Worked example, finding the length of a tube for a closed-pipe resonator.

If sound travels through the air at a speed of 344 m/s, what should be the length of a tube closed at one end to have a fundamental frequency of 128 Hz?

The length L can be found by rearranging the equation f n = n v 4 L f n = n v 4 L .

(1) Identify knowns.

The fundamental frequency is 128 Hz.
The speed of sound is 344 m/s.

(2) Use f n = n v w 4 L f n = n v w 4 L to find the fundamental frequency ( n = 1).

(3) Solve this equation for length.

(4) Enter the values of the speed of sound and frequency into the expression for L .

Many wind instruments are modified tubes that have finger holes, valves, and other devices for changing the length of the resonating air column and therefore, the frequency of the note played. Horns producing very low frequencies, such as tubas, require tubes so long that they are coiled into loops.

Finding the Third Overtone in an Open-Pipe Resonator

If a tube that’s open at both ends has a fundamental frequency of 120 Hz, what is the frequency of its third overtone?

Since we already know the value of the fundamental frequency (n = 1), we can solve for the third overtone (n = 4) using the equation f n = n v 2 L f n = n v 2 L .

Since fundamental frequency (n = 1) is

To solve this problem, it wasn’t necessary to know the length of the tube or the speed of the air because of the relationship between the fundamental and the third overtone. This example was of an open-pipe resonator; note that for a closed-pipe resonator, the third overtone has a value of n = 7 (not n = 4).

Using Beat Frequency to Tune a Piano

Piano tuners use beats routinely in their work. When comparing a note with a tuning fork, they listen for beats and adjust the string until the beats go away (to zero frequency). If a piano tuner hears two beats per second, and the tuning fork has a frequency of 256 Hz, what are the possible frequencies of the piano?

Since we already know that the beat frequency f B is 2, and one of the frequencies (let’s say f 2 ) is 256 Hz, we can use the equation f B = | f 1 − f 2 | f B = | f 1 − f 2 | to solve for the frequency of the piano f 1 .

Since f B = | f 1 − f 2 | f B = | f 1 − f 2 | ,

we know that either f B = f 1 − f 2 f B = f 1 − f 2 or − f B = f 1 − f 2 − f B = f 1 − f 2 .

Solving for f 1 ,

Substituting in values,

The piano tuner might not initially be able to tell simply by listening whether the frequency of the piano is too high or too low and must tune it by trial and error, making an adjustment and then testing it again. If there are even more beats after the adjustment, then the tuner knows that he went in the wrong direction.

Practice Problems

Check your understanding.

Use these questions to assess student achievement of the section’s Learning Objectives. If students are struggling with a specific objective, these questions will help identify it and direct students to the relevant content.

Over time the energy increases and the amplitude gradually reduces to zero. This is called damping.
Over time the energy dissipates and the amplitude gradually increases. This is called damping.
Over time the energy increases and the amplitude gradually increases. This is called damping.
Over time the energy dissipates and the amplitude gradually reduces to zero. This is called damping.
The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance, and a system being driven at its natural frequency is said to resonate.
The phenomenon of driving a system with a frequency higher than its natural frequency is called resonance, and a system being driven at its natural frequency does not resonate.
The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance, and a system being driven at its natural frequency does not resonate.
The phenomenon of driving a system with a frequency higher than its natural frequency is called resonance, and a system being driven at its natural frequency is said to resonate.

In the tuning fork and tube experiment, in case a standing wave is formed, at what point on the tube is the maximum disturbance from the tuning fork observed? Recall that the tube has one open end and one closed end.

At the midpoint of the tube
Both ends of the tube
At the closed end of the tube
At the open end of the tube

In the tuning fork and tube experiment, when will the air column produce the loudest sound?

If the tuning fork vibrates at a frequency twice that of the natural frequency of the air column.
If the tuning fork vibrates at a frequency lower than the natural frequency of the air column.
If the tuning fork vibrates at a frequency higher than the natural frequency of the air column.
If the tuning fork vibrates at a frequency equal to the natural frequency of the air column.

What is a closed-pipe resonator?

A pipe or cylindrical air column closed at both ends
A pipe with an antinode at the closed end
A pipe with a node at the open end
A pipe or cylindrical air column closed at one end

Give two examples of open-pipe resonators.

piano, violin
drum, tabla
rlectric guitar, acoustic guitar
flute, oboe

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-physics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/physics/pages/1-introduction

Authors: Paul Peter Urone, Roger Hinrichs
Publisher/website: OpenStax
Book title: Physics
Publication date: Mar 26, 2020
Location: Houston, Texas
Book URL: https://openstax.org/books/physics/pages/1-introduction
Section URL: https://openstax.org/books/physics/pages/14-4-sound-interference-and-resonance

© Jun 7, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

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Interference and Beats
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Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium. As mentioned in a previous unit of The Physics Classroom Tutorial, if two upward displaced pulses having the same shape meet up with one another while traveling in opposite directions along a medium, the medium will take on the shape of an upward displaced pulse with twice the amplitude of the two interfering pulses. This type of interference is known as constructive interference . If an upward displaced pulse and a downward displaced pulse having the same shape meet up with one another while traveling in opposite directions along a medium, the two pulses will cancel each other's effect upon the displacement of the medium and the medium will assume the equilibrium position. This type of interference is known as destructive interference . The diagrams below show two waves - one is blue and the other is red - interfering in such a way to produce a resultant shape in a medium; the resultant is shown in green. In two cases (on the left and in the middle), constructive interference occurs and in the third case (on the far right, destructive interference occurs.

But how can sound waves that do not possess upward and downward displacements interfere constructively and destructively? Sound is a pressure wave that consists of compressions and rarefactions . As a compression passes through a section of a medium, it tends to pull particles together into a small region of space, thus creating a high-pressure region. And as a rarefaction passes through a section of a medium, it tends to push particles apart, thus creating a low-pressure region. The interference of sound waves causes the particles of the medium to behave in a manner that reflects the net effect of the two individual waves upon the particles. For example, if a compression (high pressure) of one wave meets up with a compression (high pressure) of a second wave at the same location in the medium, then the net effect is that that particular location will experience an even greater pressure. This is a form of constructive interference. If two rarefactions (two low-pressure disturbances) from two different sound waves meet up at the same location, then the net effect is that that particular location will experience an even lower pressure. This is also an example of constructive interference. Now if a particular location along the medium repeatedly experiences the interference of two compressions followed up by the interference of two rarefactions, then the two sound waves will continually reinforce each other and produce a very loud sound. The loudness of the sound is the result of the particles at that location of the medium undergoing oscillations from very high to very low pressures. As mentioned in a previous unit , locations along the medium where constructive interference continually occurs are known as anti-nodes . The animation below shows two sound waves interfering constructively in order to produce very large oscillations in pressure at a variety of anti-nodal locations. Note that compressions are labeled with a C and rarefactions are labeled with an R.

Now if two sound waves interfere at a given location in such a way that the compression of one wave meets up with the rarefaction of a second wave, destructive interference results. The net effect of a compression (which pushes particles together) and a rarefaction (which pulls particles apart) upon the particles in a given region of the medium is to not even cause a displacement of the particles. The tendency of the compression to push particles together is canceled by the tendency of the rarefactions to pull particles apart; the particles would remain at their rest position as though there wasn't even a disturbance passing through them. This is a form of destructive interference. Now if a particular location along the medium repeatedly experiences the interference of a compression and rarefaction followed up by the interference of a rarefaction and a compression, then the two sound waves will continually cancel each other and no sound is heard. The absence of sound is the result of the particles remaining at rest and behaving as though there were no disturbance passing through it. Amazingly, in a situation such as this, two sound waves would combine to produce no sound. As mentioned in a previous unit , locations along the medium where destructive interference continually occurs are known as nodes .

Two Source Sound Interference

A popular Physics demonstration involves the interference of two sound waves from two speakers. The speakers are set approximately 1-meter apart and produced identical tones. The two sound waves traveled through the air in front of the speakers, spreading out through the room in spherical fashion. A snapshot in time of the appearance of these waves is shown in the diagram below. In the diagram, the compressions of a wavefront are represented by a thick line and the rarefactions are represented by thin lines. These two waves interfere in such a manner as to produce locations of some loud sounds and other locations of no sound. Of course the loud sounds are heard at locations where compressions meet compressions or rarefactions meet rarefactions and the "no sound" locations appear wherever the compressions of one of the waves meet the rarefactions of the other wave. If you were to plug one ear and turn the other ear towards the place of the speakers and then slowly walk across the room parallel to the plane of the speakers, then you would encounter an amazing phenomenon. You would alternatively hear loud sounds as you approached anti-nodal locations and virtually no sound as you approached nodal locations. (As would commonly be observed, the nodal locations are not true nodal locations due to reflections of sound waves off the walls. These reflections tend to fill the entire room with reflected sound. Even though the sound waves that reach the nodal locations directly from the speakers destructively interfere, other waves reflecting off the walls tend to reach that same location to produce a pressure disturbance.)

Destructive interference of sound waves becomes an important issue in the design of concert halls and auditoriums. The rooms must be designed in such as way as to reduce the amount of destructive interference. Interference can occur as the result of sound from two speakers meeting at the same location as well as the result of sound from a speaker meeting with sound reflected off the walls and ceilings. If the sound arrives at a given location such that compressions meet rarefactions, then destructive interference will occur resulting in a reduction in the loudness of the sound at that location. One means of reducing the severity of destructive interference is by the design of walls, ceilings, and baffles that serve to absorb sound rather than reflect it. This will be discussed in more detail later in Lesson 3 .

The destructive interference of sound waves can also be used advantageously in noise reduction systems . Earphones have been produced that can be used by factory and construction workers to reduce the noise levels on their jobs. Such earphones capture sound from the environment and use computer technology to produce a second sound wave that one-half cycle out of phase . The combination of these two sound waves within the headset will result in destructive interference and thus reduce a worker's exposure to loud noise.

Musical Beats and Intervals

Interference of sound waves has widespread applications in the world of music. Music seldom consists of sound waves of a single frequency played continuously. Few music enthusiasts would be impressed by an orchestra that played music consisting of the note with a pure tone played by all instruments in the orchestra. Hearing a sound wave of 256 Hz (middle C) would become rather monotonous (both literally and figuratively). Rather, instruments are known to produce overtones when played resulting in a sound that consists of a multiple of frequencies. Such instruments are described as being rich in tone color. And even the best choirs will earn their money when two singers sing two notes (i.e., produce two sound waves) that are an octave apart . Music is a mixture of sound waves that typically have whole number ratios between the frequencies associated with their notes. In fact, the major distinction between music and noise is that noise consists of a mixture of frequencies whose mathematical relationship to one another is not readily discernible. On the other hand, music consists of a mixture of frequencies that have a clear mathematical relationship between them. While it may be true that "one person's music is another person's noise" (e.g., your music might be thought of by your parents as being noise), a physical analysis of musical sounds reveals a mixture of sound waves that are mathematically related.

To demonstrate this nature of music, let's consider one of the simplest mixtures of two different sound waves - two sound waves with a 2:1 frequency ratio. This combination of waves is known as an octave. A simple sinusoidal plot of the wave pattern for two such waves is shown below. Note that the red wave has two times the frequency of the blue wave. Also observe that the interference of these two waves produces a resultant (in green) that has a periodic and repeating pattern. One might say that two sound waves that have a clear whole number ratio between their frequencies interfere to produce a wave with a regular and repeating pattern. The result is music.

Another simple example of two sound waves with a clear mathematical relationship between frequencies is shown below. Note that the red wave has three-halves the frequency of the blue wave. In the music world, such waves are said to be a fifth apart and represent a popular musical interval. Observe once more that the interference of these two waves produces a resultant (in green) that has a periodic and repeating pattern. It should be said again: two sound waves that have a clear whole number ratio between their frequencies interfere to produce a wave with a regular and repeating pattern; the result is music.

Finally, the diagram below illustrates the wave pattern produced by two dissonant or displeasing sounds. The diagram shows two waves interfering, but this time there is no simple mathematical relationship between their frequencies (in computer terms, one has a wavelength of 37 and the other has a wavelength 20 pixels). Observe (look carefully) that the pattern of the resultant is neither periodic nor repeating (at least not in the short sample of time that is shown). The message is clear: if two sound waves that have no simple mathematical relationship between their frequencies interfere to produce a wave, the result will be an irregular and non-repeating pattern. This tends to be displeasing to the ear.

Investigate!

A final application of physics to the world of music pertains to the topic of beats. Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another. The diagram below illustrates the wave interference pattern resulting from two waves (drawn in red and blue) with very similar frequencies. A beat pattern is characterized by a wave whose amplitude is changing at a regular rate. Observe that the beat pattern (drawn in green) repeatedly oscillates from zero amplitude to a large amplitude, back to zero amplitude throughout the pattern. Points of constructive interference (C.I.) and destructive interference (D.I.) are labeled on the diagram. When constructive interference occurs between two crests or two troughs, a loud sound is heard. This corresponds to a peak on the beat pattern (drawn in green). When destructive interference between a crest and a trough occurs, no sound is heard; this corresponds to a point of no displacement on the beat pattern. Since there is a clear relationship between the amplitude and the loudness, this beat pattern would be consistent with a wave that varies in volume at a regular rate.

Beat Frequency

The beat frequency refers to the rate at which the volume is heard to be oscillating from high to low volume. For example, if two complete cycles of high and low volumes are heard every second, the beat frequency is 2 Hz. The beat frequency is always equal to the difference in frequency of the two notes that interfere to produce the beats. So if two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a beat frequency of 2 Hz will be detected. A common physics demonstration involves producing beats using two tuning forks with very similar frequencies. If a tine on one of two identical tuning forks is wrapped with a rubber band, then that tuning forks frequency will be lowered. If both tuning forks are vibrated together, then they produce sounds with slightly different frequencies. These sounds will interfere to produce detectable beats. The human ear is capable of detecting beats with frequencies of 7 Hz and below.

A piano tuner frequently utilizes the phenomenon of beats to tune a piano string. She will pluck the string and tap a tuning fork at the same time. If the two sound sources - the piano string and the tuning fork - produce detectable beats then their frequencies are not identical. She will then adjust the tension of the piano string and repeat the process until the beats can no longer be heard. As the piano string becomes more in tune with the tuning fork, the beat frequency will be reduced and approach 0 Hz. When beats are no longer heard, the piano string is tuned to the tuning fork; that is, they play the same frequency. The process allows a piano tuner to match the strings' frequency to the frequency of a standardized set of tuning forks.

Important Note: Many of the diagrams on this page represent a sound wave by a sine wave. Such a wave more closely resembles a transverse wave and may mislead people into thinking that sound is a transverse wave. Sound is not a transverse wave, but rather a longitudinal wave . Nonetheless, the variations in pressure with time take on the pattern of a sine wave and thus a sine wave is often used to represent the pressure-time features of a sound wave.

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Check Your Understandin g

Two speakers are arranged so that sound waves with the same frequency are produced and radiate through the room. An interference pattern is created (as represented in the diagram at the right). The thick lines in the diagram represent wave crests and the thin lines represent wave troughs. Use the diagram to answer the next two questions.

a. B only b. A, B, and C c. D, E, and F d. A and B

Both points A and B are on locations where a crest meets a crest.

2. How many of the six labeled points represent anti-nodes?

a. 1

b. 2

c. 3

d. 4

e. 6

Only points A and B are antinodes; the other points are points where crests and troughs meet.

3. A tuning fork with a frequency of 440 Hz is played simultaneously with a fork with a frequency of 437 Hz. How many beats will be heard over a period of 10 seconds?

Answer: 30 beats

The beat frequency will be 3 Hz; thus in 10 seconds, there should be 30 beats.

4. Why don't we hear beats when different keys on the piano are played at the same time?

Our ears can only detect beats if the two interfering sound waves have a difference in frequency of 7 Hz or less. No two keys on the piano are that similar in frequency.

Natural Frequency

NOTIFICATIONS

Sound – wave interference.

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Sound waves are longitudinal or compression waves that transmit sound energy from the source of the sound to an observer. Sound waves are typically drawn as transverse waves, with the peaks and troughs representing the areas of compression and decompression of the air. Sound waves can also move through liquids and solids, but this article focuses on sound waves in air.

When a sound wave travels out from a source, it travels outwards like a wave produced when a stone is dropped into water. The sound wave from a single clap is similar to a stone dropped in water – the wave spreads out over time. The wave pattern formed by a series of steady vibrations would look like a series of concentric circles centred on the source of the vibration.

Detecting sound waves

Sound waves are not visible. To detect them, we can use our ears or we can position a microphone (probe) and observe the sound using an oscilloscope, computer or smartphone app.

In the image below, the microphone is detecting the sound of the note A at two different octaves – one vibrating at 440 vibrations per second and the other at 220. The number of vibrations per second is also known as frequency or pitch and is measured in hertz, which has the symbol Hz (named after Heinrich Hertz).

Notice that the wavelength for the 220 Hz wave is longer than the wavelength for the 440 Hz wave. As the wavelength increases, the frequency decreases according to the formula:

$frequency = \frac{speed\, of\, wave}{wavelength}$

Wave interference

When two or more sound waves occupy the same space, they affect one another. The waves do not bounce off of each, but they move through each other. The resulting wave depends on how the waves line up.

With constructive interference, two waves with the same frequency and amplitude line up – the peaks line up with peaks and troughs with troughs as in diagram A above. The result is a wave that has twice the amplitude of the original waves so the sound wave will be twice as loud.

Destructive interference is when similar waves line up peak to trough as in diagram B. The result is a cancellation of the waves. Noise-cancelling headphones work on this principle. They detect the sounds coming into the ear and produce sounds with equal volume but with the peaks and troughs reversed, resulting in near silence.

The result of any combination of sound waves is simply the addition of the various waves. When we hear the sound of two different musical notes, as shown in diagram C, we hear a complex waveform we think of as harmony.

Diagram D shows beats – when two sound waves are nearly the same frequency but slightly different. The resulting wave has points of constructive interference and destructive interference. A sound wave with the beat pattern in diagram D will have a volume that varies at a regular rate – you can hear a pulse or flutter in the sound.

Sound waves and pitch

Because sound travels outwards from a central source, waves interact in interesting patterns. When the same pitch or frequency sound wave is produced from two sources, a pattern of interference is produced.

In the image below, two sources – labelled Sound 1 and 2 – are aligned one above the other. The waves interfere with each other so that there is constructive interference in some areas (left-hand picture) and destructive interference in other areas (right-hand picture).

As the spacing between the sources is increased, the interference pattern changes and more zones of destructive interference are created.

These interference patterns can easily be observed by placing two sound sources in close proximity (0.5–2 metres apart) in a large open space and setting each to emit the same pitch. When you walk around listening to the sound, distinct areas of loudness and softness can be observed.

Useful link

Visit this website to view an excellent simulation of a ripple tank for demonstrating wave-related phenomena.

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