We usually think of sound waves traveling in air, but sound can travel through any gas, through liquids, and even through solids. FIGURE 16.19 shows a loudspeaker cone vibrating back and forth in a fluid such as air or water. Each time the cone moves forward, it collides with the molecules and pushes them closer together. A half cycle later, as the cone moves backward, the fluid has room to expand and the density decreases a little. These regions of higher and lower density (and thus higher and lower pressure) are called compressions and rarefactions.

FIGURE 16.19 A sound wave is a sequence of compressions and rarefactions.

This periodic sequence of compressions and rarefactions travels outward from the loudspeaker as a longitudinal sound wave. When the wave reaches your ear, the oscillating pressure causes your eardrum to vibrate. These vibrations are transferred into your inner ear and perceived as sound.

The speed of sound waves depends on the compressibility of the medium. As TABLE 16.1 shows, the speed is faster in liquids and solids (relatively incompressible) than in gases (highly compressible). For sound waves in air, the speed at temperature T (in $\text{°}\text{C}$) is

We’ll derive this result in Section 16.6, but recall from chemistry that adding 273 to a Celsius temperature converts it to an absolute temperature in kelvins. The speed of sound increases with increasing temperature but, interestingly, does not depend on the air pressure. For air at room temperature ($20\text{°}\text{C}$),

This is the value you should use when solving problems unless you’re given temperature information.

A speed of $343\text{m}\text{/}\text{s}$ is high, but not extraordinarily so. A distance as small as 100 m is enough to notice a slight delay between when you see something, such as a person hammering a nail, and when you hear it. The time required for sound to travel 1 km is $t=(1000\text{m})\text{/}\left(343\text{m}\text{/}\text{s}\right)\approx 3\text{s}$. You may have learned to estimate the distance to a bolt of lightning by timing the number of seconds between when you see the flash and when you hear the thunder. Because sound takes 3 s to travel 1 km, the time divided by 3 gives the distance in kilometers. Or, in English units, the time divided by 5 gives the distance in miles.

Your ears are able to detect sound waves with frequencies between roughly 20 Hz and 20,000 Hz, or 20 kHz. You can use the fundamental relationship $v_{\text{sound}}=\text{λ}f$ to calculate that a 20 Hz sound wave has a 17-m-long wavelength, while the wavelength of a 20 kHz note is a mere 17 mm. Low frequencies are perceived as “low-pitch” bass notes, while high frequencies are heard as “high-pitch” treble notes. Your high-frequency range of hearing can deteriorate with age (10 kHz is the average upper limit at age 65) or as a result of exposure to very loud sounds.

Sound waves exist at frequencies well above 20 kHz, even though humans can’t hear them. These are called ultrasonic frequencies. Oscillators vibrating at frequencies of many MHz generate the ultrasonic waves used in ultrasound medical imaging. A 3 MHz wave traveling through water (which is basically what your body is) at a sound speed of $1480\text{m}\text{/}\text{s}$ has a wavelength of about 0.5 mm. It is this very small wavelength that allows ultrasound to image very small objects. We’ll see why when we study diffraction in Chapter 33.