# Specifics of Sound Wave Behavior

Begin by reviewing to aspects of the wave lecture, measurable wave characteristics (frequency, amplitude, and velocity) and the basics of how waves act in the environment.

Light waves and sound waves are similar but not identical.

In general sound waves are longitudinal waves radiating outward from a source in a generally spherical pattern. The wave consists of areas of compression and rarefaction of the molecules in the conducting medium.

Frequency:

Possible Frequency: 0 Hz—Infinity Hz (Actually, there is an upper limit to sound waves on the order of 1013 Hz.)

Audible Frequency: 50 Hz -- 18,000 Hz or 18 kHz (It is highly variable among individuals.)

Ultrasonic: above human delectability (hearing), used for cleaning, measuring, camera focus, medical imaging, surgery, sonar, dental drilling, welding, and dog whistles.

Infrasonic: below human delectability (hearing), used for remote sensing acoustic weapons and perhaps in the future, elephant whistles. Earthquakes, bomb blasts, etc generate infrasonic waves.

Doppler effect: The apparent frequency of a sound reaching our ears from a moving object depends on both the frequency of the sound itself and the speed of the object generating the sound. When the object is moving toward us, its speed is added to the speed of the sound wave thus creating the appearance of a higher frequency. When the object is moving away from us, its speed is subtracted from the speed of the sound wave thus creating the appearance of a lower frequency. That is why we drop the pitch of our voices when we imitate the sound (apparent frequency shift from high to low) of a racecar passing in front of us. Try it.
If that one doesn't work well, try this one.

Velocity: depends on medium.

Air 331 m/sec (1130 ft/sec)* (it can cover a mile in about five seconds)

Helium 965 m/sec

Water 1482 m/sec (4800 ft/sec)

Glass 5640 m/sec

Steel 5960 m/sec

*At sea level, 70 degrees Fahrenheit. Faster in warmer air.

*The more elastic a substance, the faster sound waves can travel in it. Sound waves travel faster in air, water, glass, and steel respectively.

Decay: sound waves get weaker the farther they go from their source. Decay comes from loss of energy (as heat) and the spreading of the energy over a larger area.

The Law of Inverse Squares.

Simply put, doubling the distance from a sound source decreases the intensity of the sound by a factor of 4. Halving the distance from sound source increases the intensity by a factor of 4.

For you physicists and mathematicians, remember the area of a sphere is 4P R2. Doubling the radius [4P (2R)2 = 16P R2] increases the area by a factor of four meaning that the same amount of sound energy is now covering four times as much area. The initial sound strength is "diluted" by that much. For non-mathematicians, just remember that the change is much more than intuition would dictate. In fact, the effect is twice what one would expect; four times instead of two times, 1/4 instead of 1/2.

Illustration

Reflection: sound waves bounce off surfaces and they follow the same laws as things like billiard balls. That is the angle of incidence equals the angle of reflection. Sound waves leave the surface at the same angle at which they hit the surface.

Echo: a result of sound waves bouncing off of surfaces that are far enough away and regular enough to produce a weaker and distinguishable replication of the original sound. It is the kind of repetition of a sound one might hear in the Grand Canyon.

Question: why are echoes weaker than the original sound.

Reverberation: a result of sound waves bouncing off of surfaces that are near enough and/or irregular enough to produce replications of the original sound that cannot be distinguished from it. It is the kind of repetition of sound one might hear while singing in the shower.

Question: what makes reverberation different from echo? Answer the question using differences in arrival time between the original sound and reflected sound.

Reflection is both problem and opportunity. Too much reverberation can sound boomy while too little can sound dry and life less. Too much echo can be distracting while too little can sound artificial depending upon the space. Controlling reflection is a key to the operation of a parabolic microphone.

Illustration

UNC Planetarium Reception Room is a parabolic reflector.

Diffraction: the tendency of waves to bend around objects they encounter. This is to be distinguished from transmission in which sound waves pass through the object. Diffraction often produces the appearance of waves having passed through an object when in fact they have simply gone around it.

In general, the lower the frequency, the better the ability of the wave to go around an object. Higher frequency waves are more directional, and more likely to be blocked by objects in their path.

Question: you are hiking in the woods and you hear a waterfall in the distance. Describe how the sound of the waterfall changes as you move toward it. Of course, it will get louder. But what else happens? Why?

Question: Which are more likely to be useful in determining the exact direction from which a sound is coming, low frequency waves or high frequency waves? Why? Assume you cannot actually see the sound source.

More questions: what do elephants, subwoofers, and foghorns, and band practice have in common? What is the relationship between the size of a parabolic reflector and its ability to capture low frequency sound?

Illustration

Absorption: porous, non-elastic, or soft materials tend to adsorb rather than reflect sound waves. Sound absorbing materials are often used to reduce reverberation. Surfaces that adsorb sound waves are said to be "dead" while those that reflect sound waves are said to be "live."

Illustration

Question: what adjustments would you may to the reverberation characteristics of a recording studio in order to make something recorded there sound as if had been recorded outside in open field on a calm quiet day?

Diffusion: Sound waves reflecting off of or passing through irregular materials tend to be scattered and lose their coherence. The scattering is called diffusion.

Interference: Sound waves interact arithmetically at points where they coincide. The interaction can be positive or negative, constructive or destructive. Waves in phase will add. Waves out of phase will subtract. If the waves differ by just a few Hz, we may hear "beats" as they interfere with each other. Here is demonstration of beats from the Explore Science site. Draw a diagram of what you think that wave form would look like.

Illustration

Resonance: All objects have a particular frequency at which they naturally vibrate. The vibrations are not always simple and clear as with a bell but they do vibrate. When the vibration of one object sets off vibrations in another it is called resonance. If the first object is vibrating at the natural resonance frequency of the second object, the induced vibration can sometimes become quite pronounced. Hence the famous (and often apocryphal) stories about opera singers who break wine glasses with their voices.

Illustration

Displacement: Sound waves have the ability physically to move objects, that is, to displace them. This is the key to our ability to detect, record, reproduce, and transmit audio material. Much more about this when we talk about transducers.

Refraction: This is the bending of a wave as it passes from one medium to another. It is most commonly thought of as related to light (lenses, prisms, fish in the water, etc). More when we get to details on light waves. Nevertheless, sound waves can be refracted by passing through the interface between to different media or, more commonly, by passing through the interface between two different states of the same medium. The nighttime condition in which the air near the ground is cooler than the air higher up (temperature inversion) results in sound traveling long distances at night. We sometimes hear cars on far away freeways or conversations from across a lake under these conditions.

Illustration

Polarization: This is an issue with light (transverse wave). Longitudinal waves do not show polarization.