Human ear In the human ear (shown in Figure 20.30), the exterior ear flap, called th...

Human ear In the human ear (shown in Figure 20.30), the exterior ear flap, called the pinna, gathers and guides sound waves into the auditory canal. The sound waves create a pressure variation at the eardrum, a variation that is about two times as great as it would be without the pinna and auditory canal. This pressure variation causes the eardrum to vibrate. A large fraction of the vibrational energy is transmitted through the three small bones in the middle ear called the hammer, anvil, and stirrup. These three bones, collectively known as the ossicles, constitute a lever system that increases the pressure exerted on a small membrane of the inner ear known as the oval window. The pressure increase is possible for two reasons. (1) The hammer feels a small pressure variation over the large area of its contact with the eardrum, whereas the stirrup exerts a large pressure variation over the small area of its contact with the oval window. This difference in areas increases the pressure by a factor of 15 to 30. (2) The three bones act as a lever that increases

the force that the stirrup exerts on the oval window, although the displacement resulting from the force is less than if the bones were not present. Because of these effects, pressure fluctuation of the stirrup against the oval window can be 180 times greater than the pressure fluctuation of a sound wave in air before it reaches the ear. The increased pressure fluctuation against the oval window causes a fluctuating pressure in the fluid inside the cochlea of the inner ear. The fluctuating pressure is sensed by nerve cells along the basilar membrane. Nerves nearest the oval window respond to high-frequency sounds, whereas nerves farther from the window respond to low-frequency sounds. Thus, our ability to distinguish the frequency of a sound depends on the variation in sensitivity of different cells to different frequencies along the basilar membrane. The basilar membrane is only about 3 cm long, and yet a normal ear can distinguish sounds that differ in frequency by about 0.3%. This ability to distinguish sounds of slightly different frequency spans the human hearing range from about 20 Hz to 20,000 Hz.

The human ear can detect sound waves whose intensity is about 10^-12 W/m². Where should you be with respect to a stereo speaker that produces sound of intensity 10^-5 W/m² when 1 m from the speaker if you do not want to listen to the music?

(a) About 3 m away

(b) About 30 m away

(c) About 3 km away

(d) It depends on the size of the speaker.