Properties of Sound

There are four properties and phenomena of sound that we should be familiar with. They are beats, loudness and intensity, Doppler effect, and sonic booms. This lesson provides an overview for each, but you really need to check out the linked documents for more in-depth information.

When two frequencies fairly close to each other interfere, there is a pattern of constructive and destructive interference (out of phase - no sound is heard) that is set up. The constructive interference (in phase - sound is louder) will actually produce a third frequency that is the algebraic difference of the two basic frequencies. This is called a beat frequency. The beat frequency is what musicians sometimes use to tune their instruments. Holding a tuning fork vibrating at the desired frequency next to a string that is just off that frequency will produce a beat. The string is adjusted until the beat disappears. Beat frequency between two frequencies (f1 and f2) is given by the formula:

For more on beat frequencies, try:

And for a couple of really good beat applets, try  or

Make sure your speakers are turned up!

Loudness is how the ear perceives the energy in sound, and it is related to the Intensity of the sound. Intensity is:

Intensity the rate of transfer of energy of a plane wave as it passes through a unit area and is measured in Watts/meter squared, or W/m2. The quietest or least intense sound that most people can hear is called the threshold of hearing and has a power level of 1*10-12 W/m2. At the other end is the level above which damage to the eardrum can become permanent. This power level is 1 W/m2 and we call this the threshold of pain.

There is a rather large difference between these two intensity levels, and it is a rather inconvenient scale to work with. A different system of measurement is used to quantify how loud something is: the Bel (B) (named for Alexander Graham Bell.) This scale is a logarithmic scale, and the unit we most frequently use is the decibel (dB), or tenth of a Bel. The intensity level (b) of any sound is given by the formula: 

where I is the intensity of the sound and Io is the reference level sound (usually 1 x 10-12 W/m2 unless comparing two values). Because this is a log scale, we need to be careful. For example, doubling the intensity of a sound is a +3dB change to the loudness. (A noise at 80 dB that suddenly becomes twice as loud would now register at 83
dB). Be sure when you are working problems you know if you need to be manipulating intensity or loudness.

Here is table of intensity level of various sounds.

Source of the

  level in dB

Intensity in

Jet plane at



Threshold of



Loud indoor
  rock concert



Busy street






Threshold of



For more on loudness and intensity, try:


Doppler Effect is an apparent change in frequency of a sound due to relative motion between the source of the sound and an observer. Doppler occurs for all types of waves, but we notice it more for sound. Think of when you have heard an approaching siren. The pitch of the siren is steady and high, but as soon as the siren passes you, there is a dramatic decrease in the pitch (don't confuse this with a change in loudness as the siren comes closer then moves away.) There are two basic cases of doppler and two versions of each case. In the first case, the observer is stationary and the source is moving towards or away from the observer. Here, it is as if the sound waves that you are hearing are being stacked one on top of another (pitch rises) or stretched out (pitch falls), depending on if the source is approaching or leaving. For these two cases, the doppler formula is given by:

Observer stationary, source approaching:

Observer stationary, source leaving:

Where f is the base frequency of the sound, f' is the apparent frequency of the sound, v is the speed of sound, vo is the speed of the observer, and vs is the speed of the source. In the second case, the source is stationary but the observer is moving towards or away from the source. In this instance, the formulas are a little simpler because you are merely adding or subtracting the observer's velocity to the speed of sound. The formulas are given by:

Source stationary, observer moving approaching source:

Source stationary, observer moving away from source:

For a little more in-depth view of Doppler effect, with some pictures and applets, try:

This brings us to the final topic - sonic booms. When an object travels faster than the speed of sound in the medium (supersonic), a shockwave is set up as the sound waves "pile up" in front of the object. These waves will combine to form one wave with a very large crest and a very large trough. An observer will hear this as a very loud boom (sonic boom) that contains a great deal of energy - often enough to beak glass in nearby buildings. We generally associate this phenomenon with jets and rockets. As a plane approaches this speed, we say it is transonic. As it goes supersonic, we say it "breaks the sound barrier". Speeds above this are often recorded in Mach, where 1 Mach is the speed of sound in air. A plane that is traveling at Mach 2.5 is going two and a half times the speed of sound.

The NTNU Virtual Physics Laboratory provides several excellent applets that demonstrate principles of Physics. Click Here for an applet you can run from the NTNU Virtual Physics Laboratory that will help with your  Understanding of the Doppler Effect and Sonic Booms.


Click Here to see an applet that helps you locate an airplane after hearing a sonic boom.


Want to see a sonic boom? Click Here for a great picture!


For Practice Problems, Try: Giancoli Multiple Choice PracticeQuestions (All Questions)