Sound with frequencies below about 50 Hz may be felt by our bodies rather than heard by our ears. Such very low frequencies are called infrasonic. Sound with frequencies above our hearing sensitivity are known as ultrasonic. Dogs can hear much higher frequencies than humans; that is why a dog whistle may not be heard by humans. Sound with these ultrasonic frequencies are used for such things a sonograms that give a picture of the inside of a person's body without requiring surgery. Sonograms, like the one in Figure 12.1, are common during pregnancies but they are also used in diagnosing tumors and other conditions. Ultrasound can also be used as therapy, such as in disolving or breaking up gall stones or kidney stones.

Bats use ultrasound with a frequency of about 50,000 Hz (50 kHz) to 100,000 Hz (100 kHz). They then listen for an echo or sound reflected from flying insects. They then use this echolocation to find their evening meal-or to avoid obstacles such as walls or hanging stalagtites inside a pitch dark cave. Dolphins use a similar method of echolocation to find their way underwater.

Sound travels in air at 23¡C at about 345 m/s. For each increase in air temperature of one degree, the speed of sound increases 0.6 m/s. This is as we might expect since the air molecules move faster with increased temperature. Since the air molecules collide with other air molecules faster, they transmit the wave motion of the sound faster, too.

Sound travels through liquids and solids, too. The molecules in liquids and solids are much closer together than in a gas (like air) so the speed of sound is much higher in liquids and solids. The speed of sound in water is about 1500 m/s. The speed of sound in steel is about 5000 m/s. Geologists detonate small explosions and measure the speed and other characteristics of the sound waves that travel through the Earth from the explosion to determine characteristics of the material under the Earth. Doing this they may find fault lines or deposits of petroleum or minerals or underground water reservoirs. You might think of this as a crude sonogram of the interior of the Earth.

Just as beauty is in the eyes of the beholder, it is certainly true that music is in the ears of the beholder since one person's music is another person's noise. Yet there are objective descriptions that we can apply to sounds of various kinds.

In general we can say that noise-like the crash of a trash can-is sound that is not periodic. That means that the sound wave does not repeat itself. A musical sound is periodic; there is a repeatable pattern. We can connect a microphone to an oscilloscope or a computer interface in order to see the sound waves we want to talk about. If we do that, Figure 12.2 illustrates what we might see for the sound waves of noise and of a musical sound.

Perhaps the first characteristic of any sound we notice is its loudness. The racket of a jackhammer or the softness of a whisper come to mind. The loudness of a sound is connected to the amplitude of the sound wave. When we studied periodic motion and waves in the previous two chapters, we found that the energy of a mass and spring or the energy of a pendulum or the energy of a wave is proportional to the square of the amplitude of the motion. A louder sound means the air molecules are moving with a greater amplitude and they, in turn, cause your ear drum to move with a larger amplitude. A louder sound carries more energy per time across some area (like your ear drum). This value of energy per time per area, or power per area, is called the intensity of the sound wave. This is illustrated in Figure 12.3.

Our ears are sensitive over an incredible range of loudness. The softest whisper you can hear has a sound intensity of about 10-12 W/m2. Voices in ordinary conversation carry a sound intensity of about 10-6 W/m2. A jackhammer makes noise which has a sound intensity of about 10-3 W/m2. Pain, and damage to the ear, starts at about 1 W/m2. Loudness is quite subjective. If you consider two sounds such that most people will describe the first one as "about twice as loud as" the second, we will find that the sound intensity of the first is nearly ten times that of the second. We might describe that by saying our ears are not linear in their response to sound.

Sound from a point source-a small loudspeaker or your mouth, many or most sources-spreads out in a spherical wave front as shown by Figure 12.4. The power (energy per time) initially supplied to the sound is spread over the spherical wave front that gets larger as the square of the radius of the sphere. That means the sound intensity reaching your ear (or a microphone) decreases as one over the square of the distance away from the from the source (1/r2). If you move twice as far away, the sound intensity is one fourth. If you move ten times as far away, the sound intensity is one one-hundredth. Since our ears are non-linear, this decrease in sound level is noticeable but not as drastic as the values of the sound intensity might indicate.