phy1020.DVI

Chapter 11

Sound

Soundconsists of longitudinal waves that propagate through some medium and may be detected by the human
ear. We often think of sound waves as propagating through the air, but sound waves may also move through
other materials like helium, water, or steel. In this chapter we’ll examine a few of the basic properties of
sound waves.

11.1 Speed of Sound

First of all, how fast do sound waves travel? You’ve probably noticed that sound waves have a noticeable
travel time—for example, when you’re watching a baseball game far from home plate, there is a definite
delay betweenseeinga batter hit the ball, andhearingthe sound. Experimentally, we find the nominal speed
of sound in air to be (at 20 ıC)

vsndD 343 m=s (11.1)

It turns out that the speed of sound is strongly dependent on temperature. An empirical formula that corrects
for this temperature variation gives the speed of sound in air as

vsnd.331C0:60Tc/m=s; (11.2)

whereTcis the air temperature, inıC. Notice that ifTcD 20 ıC, we get 343 m/s.
If we convert units, we find that this is equal to about^1 / 5 mile per second. This gives the rule you may have
learned in childhood for estimating the distance of a lightning flash: after you see the lightning, count how
many seconds go by before you hear the thunder, then divide by 5 to find how many miles away the lightning
was. (Light travels about 900,000 times faster than sound, so the lightning reaches you almost instantly, and
you don’t need to consider the light travel time.)
What about the speed of sound in other materials? Recall from Eq. (9.4) that the speed of waves in a
string is the square root of the tension divided by the density:vD

p
FT=.m=L/. The speed of sound waves
in fluids follows a similar formula, known as theNewton-Laplace equation:

vsndD

s

B

; (11.3)

whereBis called thebulk modulusof the material (a measure of its compressibility), and is the density
of the material. Table 11-1 shows the bulk moduli, densities, and speeds of sound for several different
fluids. (For the speed of sound insolids, you use theYoung’s modulusYin place of the bulk modulusB:
vsndD

p

Y=.)