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The decibel scale is used because it closely corresponds to how we perceive the loudness of sounds. The human ear is really quite an amazing detector of sound, and it's worth spending some time learning how it works.
The ear is split into three sections, the outer ear, the middle ear, and the inner ear. The outer ear acts much like a funnel, collecting the sound and transferring it inside the head down a passage that's about 3 cm long, ending at the ear drum.
The ear drum separates the outer ear from the middle ear, and, much like the skin on a drum, it is a thin membrane that vibrates in response to a sound wave. The middle ear is connected to the mouth via the eustachian tubes to ensure that the inside of the eardrum is maintained at atmospheric pressure. This is necessary for the drum to be able to respond to the small variations in pressure from atmospheric pressure that make up the sound wave.
In the middle ear are three small bones, called the hammer, anvil, and stirrup because of their shapes. These transfer the sound wave from the ear drum to the inner ear. Similar to a hydraulic lift, the pressure is transferred from a relatively large area (the eardrum) to a smaller area (the window to the inner ear). By Pascal's principle (see the section on fluids), the pressure is constant. The force is smaller at the small-area inner ear, but the work done at each end is equal, so the inner ear experiences a vibration with a much larger amplitude than that at the ear drum. The bones, in effect, act as an audio amplifier.
The eardrum and the window to the inner ear have different acoustic properties. If they were directly connected together some energy would be reflected back. The three bones in the middle ear are designed to transfer sound energy from the eardrum to the inner ear without any energy lost to reflections. The technical physics term for this is "impedance match": any time energy is transferred from one system to another without any reflected energy, the impedances are matched at the transfer point...in this case, the bones provide the impedance matching. The bottom line is that they will amplify the sound level without losing any sound energy.
The inner ear contains a fluid-filled tube, the cochlea. The cochlea is coiled like a snail, is about 3 mm in diameter, and is divided along its length by the basilar membrane. It also contains a set of hair cells that convert the sound wave into electrical pulses; these are transferred along nerves to the brain, to be interpreted as sound. When a sound signal enters the inner ear, a small movement of the basilar membrane or the fluid in the cochlea results in the rubbing of another membrane across the hair cells. The relatively long hairs provide another level of amplification, in the sense that a small force applied at the ends is converted into a relatively large torque.
To summarize, then, the outer ear collects sound and transfers it to the middle ear; the middle ear amplifies the sound and passes it to the inner ear; and the inner ear converts the sound into electrical signals to be sent to the brain.
The range of human hearing is quite large, both in terms of sound intensity and sound frequency. Humans can hear sounds between about 20 Hz and 20000 Hz; music and speech typically covers the range from 100 Hz to 3000 Hz. The ear is most sensitive to sound of about 3000 Hz, as the following graph shows:
The Doppler effect describes the shift in the frequency of a wave sound when the wave source and/or the receiver is moving. We'll discuss it as it pertains to sound waves, but the Doppler effect applies to any kind of wave. As with ultrasound, the Doppler effect has a variety of applications, ranging from medicine (with sound) to police radar and astronomy (with electromagnetic waves).
The Doppler effect is something you're familiar with. If you hear an emergency vehicle with its siren on, you notice an abrupt change in the frequency of the siren when it goes past you. If you are standing still when the vehicle is coming toward you, the frequency is higher than it would be if the vehicle was stationary; when the vehicle moves away from you, the frequency is lower. A similar effect occurs if the sound source is stationary and you move toward it or away from it.
At first glance you might think that there should be no difference between what happens when you move at a particular speed toward a source and when the source moves at the same speed toward you. As long as the speed is much less than the speed of sound, there is hardly any difference between these two cases. The higher the speeds involved, however, the greater the difference.
To convince yourself that it does make a difference which is moving, the source or the observer, consider what happens when v is equal to the speed of sound. When the receiver moves at the speed of sound toward the source, twice as many waves are intercepted as by a stationary observer, and the frequency is doubled. The waves are still nicely separated, however. On the other hand, when the source moves toward the receiver at the speed of sound, the sound waves pile up on top of each other (resulting in a sonic boom), and the frequency is effectively infinite.
Consider first the case of a stationary source, and an observer (you, for example) moving toward the source. As shown in the diagram, the waves are emitted by the source uniformly.
If the observer is stationary, the frequency received by the observer is the frequency emitted by the source:
If the observer moves toward the source at a speed vo, more waves are intercepted per second and the frequency received by the observer goes up. Effectively, the observer's motion shifts the speed at which the waves are received; it's basically a relative velocity problem. The observed frequency is given by:
If the observer is stationary but the source moves toward the observer at a speed vs, the observer still intercepts more waves per second and the frequency goes up.
This time it is the wavelength of the wave received by the observer that is effectively shifted by the motion, rather than the speed. The effective wavelength is simply:
The frequency of waves received by the observer is then:
In the most general case, in which both the source and receiver are moving, the observed frequency is:
Sonic booms occur when the source travels faster than the speed of sound. If the source is traveling at the speed of sound, the waves pile up and move along with the source; when the source travels faster than sound, a shock wave (also known as a sonic boom) occurs as waves pile up. The angle at which the shock wave moves away from the path of the source depends on the speed of the source relative to the speed of sound.
A source is traveling east at 10 m/s toward you; you're traveling at 2 m/s east. It's 20 °C. When the source is not moving it emits sound of frequency 3000 Hz. What frequency do you hear?
Sound in air at 20 °C travels at 343 m/s. Plugging all of this information into the equation, and making sure we get the signs right, gives:
Interference is what happens when two or more waves come together. Depending on how the peaks and troughs of the waves are matched up, the waves might add together or they can partially or even completely cancel each other. We'll discuss interference as it applies to sound waves, but it applies to other waves as well.
The principle of linear superposition - when two or more waves come together, the result is the sum of the individual waves.
The principle of linear superposition applies to any number of waves, but to simplify matters just consider what happens when two waves come together. For example, this could be sound reaching you simultaneously from two different sources, or two pulses traveling towards each other along a string. When the waves come together, what happens? The result is that the waves are superimposed: they add together, with the amplitude at any point being the addition of the amplitudes of the individual waves at that point.
Although the waves interfere with each other when they meet, they continue traveling as if they had never encountered each other. When the waves move away from the point where they came together, in other words, their form and motion is the same as it was before they came together.
Constructive interference occurs whenever waves come together so that they are in phase with each other. This means that their oscillations at a given point are in the same direction, the resulting amplitude at that point being much larger than the amplitude of an individual wave. For two waves of equal amplitude interfering constructively, the resulting amplitude is twice as large as the amplitude of an individual wave. For 100 waves of the same amplitude interfering constructively, the resulting amplitude is 100 times larger than the amplitude of an individual wave. Constructive interference, then, can produce a significant increase in amplitude.
The following diagram shows two pulses coming together, interfering constructively, and then continuing to travel as if they'd never encountered each other.
Another way to think of constructive interference is in terms of peaks and troughs; when waves are interfering constructively, all the peaks line up with the peaks and the troughs line up with the troughs.
Destructive interference occurs when waves come together in such a way that they completely cancel each other out. When two waves interfere destructively, they must have the same amplitude in opposite directions. When there are more than two waves interfering the situation is a little more complicated; the net result, though, is that they all combine in some way to produce zero amplitude. In general, whenever a number of waves come together the interference will not be completely constructive or completely destructive, but somewhere in between. It usually requires just the right conditions to get interference that is completely constructive or completely destructive.
The following diagram shows two pulses interfering destructively. Again, they move away from the point where they combine as if they never met each other.
