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Resonance – This 30 minute long video from The Mechanical Universe series demonstrates the concept of resonance using the notable Tacoma Narrows Bridge disaster. (Note: there is some consensus by experts that resonance was not the cause of the Tacoma Narrows Bridge disaster, but instead a concept called aeroelastic flutter, which is too complicated to discuss in this class. That said, this video is still very interesting and has lots of good scientific information about resonance.)

Acoustic levitation – Styrofoam beads are levitated in the interference patterns created in sound waves.

Video Transcript

Hello there! Welcome to lecture 20: sound.

Sound waves are vibrations of increasing and decreasing pressure that travel though some type of medium: a solid, liquid, or gas. Sound waves are of great interest not only in audio and music applications, but also in how sound waves can cause objects to resonate and cause amplification of energy.

Each of the following concepts will be discussed in this video: sound waves, the speed of sound, reflection and refraction, interference and beats, and forced vibration and resonance.

Sound waves

Sound waves are longitudinal waves that are caused by changes in air pressure between two points. Because sound waves are caused by pressure disturbances, they require some kind of medium to travel through. If you are listening to the audio on this lecture, very likely the sound waves are traveling through the air between your computer speakers or headphones and your ear drum.

Speakers turn an electrical signal into vibrations. On this speaker, I’ve placed some small pieces of paper. As I turn on the sound source, the speaker membrane vibrates back and forth. The frequency of the source controls how quickly these vibrations occur. At low frequencies, it is easy to see the pieces of paper moved around by the vibrations.

The frequency of a sound wave controls the pitch of that wave. In this demo, I’ve increased the frequency of a sound wave, and you can hear as the pitch increases as well. I’ve also used a microphone to capture the sound waves and show the pressure versus time graph for the waves. You can see the oscillations occur more and more frequently as the frequency increases.

The amplitude of a sound wave is proportional to the loudness, or volume, of that wave. In this demo, I keep the frequency constant and instead change the amplitude of the wave. As the amplitude increases, the volume increases. The microphone captures the sound waves to show the pressure vs. time graphs. The frequency of oscillation remains constant, but the amplitude increases with volume.

Musical instruments work by creating vibrations: sound waves. Different types of instruments create sound waves differently: by creating a vibration in a string, by blowing air across a reed or a mouthpiece, or by creating vibrations on a membrane stretched over a drum. The quality of the sound waves, known as timbre, is produced by the materials, design, and quality of the instrument itself.

Large instruments (such as a tuba or a bass violin) are capable of supporting standing waves with a large wavelength. Small instruments (such as a piccolo or kazoo) support standing waves with small wavelengths. Because of the relationship between frequency, wavelength, and wave speed, we can see that large instruments will create sound waves with low frequencies, and small instruments will create sound waves with high frequencies. This explains why large instruments create low-pitch sounds and why small instruments create high-pitch sounds.

Humans are capable of hearing sounds that range from very low pitch to very high pitch. Our range of hearing is approximately 20 Hz to 20,000 Hz. This of course varies from person to person, and changes as we age. Starting around 30 years old, the higher range of our hearing tends to degrade. This means that the older you are, the lower the frequency of your upper range of hearing will be. That means a high-pitched noise that bothers a young person may not even be audible to an adult.

Sound waves that have frequencies above 20,000 Hz are known as ultrasonic. Ultrasound is used in many applications in our lives. The motion detectors I have used to create many of the demos in these lecture videos and experiments in our labs use an ultrasonic wave that reflects off the nearest surface and bounces back to the detector. Ultrasound is also used frequently in medical diagnostics and imaging.

Sound waves that have frequencies below 20 Hz are known as infrasonic. Many natural sources such as earthquakes, volcanoes, and waterfalls emit infrasound. Infrasound detectors can therefore be used to monitor these phenomena.

The speed of sound

How fast do sound waves travel? That’s a simple question with a somewhat complicated answer. Because sound waves are pressure vibrations that move through a medium, the speed that those vibrations move is dependent on the medium. Lots of things can affect the speed of sound.

Firstly, let’s consider what happens to the speed of sound in different phases of matter. Sound waves travel when molecules bump into each other, transmitting energy from one place to another. If molecules are spaced closer together, then the speed of sound will be faster than if molecules are spaced far apart. This means that sound travels fastest through solids, where molecules are tightly packed, and slowest through gases, where molecules are very far apart. The speed of sound through a liquid will be somewhere in between. Sound waves will not travel at all through a vacuum, as there are no molecules present to cause pressure vibrations.

Most of the time, I’m guessing, we experience sound waves as they move through air: a gas. So what is the speed of sound in air? There is no one answer to this question. The biggest factor that influences the speed of sound in air is the temperature. To a small degree, things such as humidity and wind speed can affect the speed of sound as well. 

In this class, we will use an equation to determine the speed of sound in air. This equation was experimentally derived, and air temperature is the independent variable. The equation states that the speed of sound at a given temperature is equal to 331 meters per second plus 0.6 times T, where T is the temperature in degrees Celsius.

Room temperature is approximately 20 degrees Celsius. Let’s use the equation to determine the speed of sound at that temperature. 331 meters per second plus 0.6 times 20 is equal to 331 plus 12, which gives a speed of 343 meters per second.

The speed of sound is much, much slower than the speed of light. This is why we may see things that are far away and notice that the sound of the object is out of synch with what we see. For example, somebody playing basketball may dribble the ball, and the sound of the ball bouncing off of the ground will reach our ears after the ball actually bounces. The farther away something is, the more pronounced the effect will be.

Note that the speed of sound does NOT depend on the properties of the wave itself: frequency and amplitude do not affect the speed of sound. If I speak louder or softer, that does not change how quickly it will take the sound of my voice to reach the microphone in this recording studio.

Reflection and refraction

When waves travel, they can change their motion and properties in different ways. One thing that can happen with waves is called reflection. This occurs when waves bounce off of a surface. If you’ve looked in a mirror, you’ve experienced the reflection of light waves. Sound waves can reflect as well. When discussing sound waves, a reflection is sometimes called an echo, especially when a sound wave reflects off of a surface that is far away, causing a delay between the initial sound source and the reflected wave.

The reflection of ultrasonic waves is frequently used to determine the distance between two objects. If the temperature is known, the speed of sound can be calculated, and the amount of time it takes for a wave to leave an ultrasonic sensor, bounce off of an object, and return to the sensor can be used with the velocity equals distance divided by time equation to determine distance. In fact, this is how the motion sensors used in many lectures and labs in this class operate!

It is also possible for sound waves to refract, or bend. This happens when the speed of sound changes, for example, if there is a big temperature difference that a sound wave travels through. We will discuss the concept of refraction in more detail in lecture 28 in the context of light waves.

Interference and beats

Because sound waves are waves, they can also interfere. This can cause strange things to happen acoustically when sound waves reflect off of surfaces, say, in a concert hall. It’s possible that waves can constructively and destructively interfere in ways that cause an orchestra or band to sound strange at certain positions in a concert hall. Acoustic spaces such as concert halls are usually designed with strangely shaped panels designed to randomly reflect sound waves such that interference is unlikely to occur, and members of the audience can enjoy the sounds of the music without any interference effects.

The interference of sound waves leads to another effect: beats. Beats occur when two sound waves of very similar frequency interfere with each other. This interference creates an interesting wave that has an amplitude that increases and decreases, and sounds like WAH WAH WAH WAH WAH. As the frequencies of two interfering waves become closer together, our ears eventually become capable of hearing the two different pitches together as a single musical tone.

Here I have two sound sources at frequencies of 480 Hz and 489 Hz. Perhaps you can hear the sound of the beat, which comes across as an increase and decrease in the sound of the tones. When I turn off one of the sound sources, the interference stops and you can hear just one pure tone. When I only turn on the second sound source, again, you can just hear that pure tone. It is only when the two similar tones play at the same time that the beat is present. 

I recorded the sound sources using LoggerPro. Both of the pure tones show a normal oscillation with a constant amplitude, at the frequency of each individual sound source. When I recorded the sound sources playing together, the graph shows a very fast oscillation superimposed with a slow oscillation. That slow oscillation is the beat oscillation and is caused by the interference of the two waves.

The frequency of a beat can be calculated using an equation. The frequency of the beat is equal to the absolute value of one frequency subtracted from the other. In the case of our audio example, the beat frequency is the absolute value of 489 Hz minus 480 Hz, which is 9 Hz.

We can verify this answer by looking at the amount of time between two peaks on the beat and converting that to a frequency. One crest occurs at 0.13 seconds, and the other at 0.02 seconds. The period of the beat is therefore 0.11 seconds. Frequency is equal to one divided by period, in this case 9 Hz.

Forced vibration and resonance

A forced vibration occurs when one object causes another object to vibrate at a certain frequency. Striking a tuning fork with a mallet causes it to vibrate. There is energy in these vibrations. After striking the tuning fork, I placed it into a beaker of water. The water splashes out of the beaker, which is a great visual indication of the energy stored in the tuning fork after being forced to vibrate.

When I get a tuning fork to vibrate, I can place it on a table and cause the table to vibrate at the same frequency as the tuning fork. Plucking a guitar string causes the body of the guitar to vibrate as well, providing another example of forced vibration.

On the other hand, the natural frequency of an object refers to the frequency of the sound wave that object will tend to produce. The natural frequency of an object relates to its size and shape. Different sized tuning forks will produce different sounds.

If an object is forced to vibrate at its natural frequency, that phenomenon is known as resonance. During resonance, energy is amplified. One example of this can be demonstrated by swinging on a swing set. If you pump your legs at the natural frequency, then the amplitude of your swing will be increased.

In this demo, two sets of three pendulums with different lengths are connected by a tube. When I get the largest pendulum swinging, it moves back and forth at its natural frequency. That vibration travels through the tube and excites the identical pendulum on the other side, causing it to move back and forth as well. This forced vibration from the left-hand pendulum is equal to the natural frequency of the right-hand pendulum, so resonance occurs and both pendulums continue to move. The two smaller pendulums also experience that forced vibration, but do not start to move because they have different natural frequencies.

I can repeat this experiment by moving the middle pendulum, which causes the middle pendulum to oscillate on the other side. The same phenomenon happens with the small pendulum. Resonance occurs when the forced vibration is equal to the natural frequency of the object.

Standing waves, which we discussed in lecture 19, also demonstrate the phenomenon of resonance. This can occur in any system that can oscillate: the coiled rope used to show standing waves in lecture 19, the strings or cavities of a musical instrument, our vocal chords, and even a standing wave excited in a glass bottle.

Resonance is a phenomenon that is also seen in other physical properties, not just sound. Lasers use optical resonance to create strong beams of coherent light. Electric circuits use resonance to tune to radio or television stations. 

While resonance can be used in many beneficial applications, because resonance leads to an amplification of energy, it also becomes an area where we must be cautious. If energy is left to amplify too much, the energy build-up within the object undergoing resonance may eventually cause it to break apart. If an object such as a bridge or structure is caused to vibrate at its resonant frequency, it may collapse. Engineers take this into consideration when designing buildings, bridges, airplanes, and other structures.

Thanks for taking the time to learn about sound! Until next time, stay well.