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You can see why this would make hooking your speakers up out of phase a bad idea. If you hook them up out of phase the waves start with a phase di erence of π – one speaker is pushing out while the other is pulling in. If you sit equidistant from the two speakers and then harmonic waves with the same frequency from a single source coming from the two speakers cancel as they reach you (usually not perfectly) and the music sounds very odd indeed, because other parts of the music are not being played equally from the two speakers and don’t cancel.
You can also see that there are many other situations where constructive or destructive interference can occur, both for sound waves and for other waves including water waves, light waves, even waves on strings. Our “standing wave solution” can be rederived as the superposition of a leftand right-travelling harmonic wave, for example. You can have interference from more than one source, it doesn’t have to be just two.
This leads to some really excellent engineering. Ultrasonic probe arrays, radiotelescope arrays, sonar arrays, di raction gratings, holograms, are all examples of interference being put to work. So it is worth it to learn the general idea as early as possible, even if it isn’t assigned.
11.8: The Ear
Figure 139: The anatomy of the human ear.
Figure 139 shows a cross-section of the human ear, our basic transduction device for sound. This is not a biology course, so we will not dwell upon all of the structure visible in this picture, but rather will concentrate on the parts relevant to the physics.
Let’s start with the outer ear. This structure collects sound waves from a larger area than the ear canal per se and reflects them down to the ear canal. You can easily experiment with the kind of amplification that results from this by cupping your hands and holding them immediately behind your ears. You should be able to hear both a qualitative change in the frequencies you are hearing and an e ective amplification of the sounds from in front of you at the expense of sounds originating behind you. Many animals have larger outer ears oriented primarily towards the front, and have muscles that permit them to further alter the direction of most favorable sound collection without turning their heads. Human ears are more nearly omnidirection.
The auditory canal (ear canal in the figure above) acts like a resonant cavity to e ectively amplify frequencies in the 2.5 kHz range and tune energy deliver to the tympanic membrane or
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eardrum. This membrane is a strong, resilient, tightly stretched structure that can vibrate in response to driving sound waves. It is connected to a collection of small bones (the ossicles) that conduct sound from the eardrum to the inner ear and that constitute the middle ear in the figure above. The common name of the ossicles are: hammer, anvil and stirrup, the latter so named because its shape strongly resembles that of the stirrup on a horse saddle. The anvil e ectively amplifies oscillations by use of the principle of leverage, as a fulcrum attachment causes the stirrup end to vibrate through a much larger amplitude than the hammer end. The stirrup is directly connected to the oval window, the gateway into the inner ear.
The middle ear is connected to the eustachian tube to your throat, permitting pressure inside your middle ear to equalize with ambient air pressure outside. If you pinch your nose, close your mouth, and try to breath out hard, you can actually blow air out through your ears although this is unpleasant and can be dangerous. This is one way your ears equilbrate by “popping” when you ride a car up a hillside or fly in an airplane. If/when this does not happen, pressure di erences across the tympanic membrane reduce its response to ambient sounds reducing auditory acuity.
Figure 140: A cross-section of the spiral structure of the cochlea.
Sound, amplifed by focal concentration in the outer ear, resonance in the auditory canal, and mechanical leverage in the ossicles, enters the cochlea, a shell-shaped spiral that is the primary organ of hearing that transduces sound energy into impulses in our nervous system through the oval window. The cochlea contains hair cells of smoothly varying length lining the narrowing spiral, each of which is resonant to a particular auditory frequency. The arrangement of the cells in a cross-section of the cochlea is shown in figure 140.
The nerves stretching from these cells are collected into the auditory nerve bundle and from thence carries the impulses they give o when they receive sound at the right frequency in to the auditory cortex (not shown) where it becomes, eventually and through a process still not fully understood, our perception of sound. Our brains take this frequency resolved information – the biomechanical equivalent of a fourier transform of the sound signal, in a way – and synthesize it back into a detailed perception of sound and music within the general frequency range of 10 Hz to 20,000 Hz.
As you can see, there are many individual parts that can fail in the human auditory system. Individuals can lose or su er damage to their outer ears through accident or disease. The ear canal can become clogged with cerumen, or earwax, a waxy fluid that normally cleans and lubricates the ear canal and eardrum but that can build up and dry out to both load the tympanic membrane so it becomes less responsive and physically occlude part of the canal so less sound energy can get through. The eardrum itself is vulnerable to sudden changes in sound pressure or physical contact that can puncture it. The middle ear, as a closed, warm, damp cavity connected to the throat, is an ideal breeding ground for certain bacteria that can cause infections and swelling that both interfere with or damage hearing and that can be quite painful. The ossicles are susceptible to physical
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trauma and infectious damage.
Finally, the hair cells of the cochlea itself, which are safely responsive over at least twelve to fourteen orders of magnitude of transient sound intensity (and safely responsive over eight or nine orders of magnitude of sustained sound intensity) are highly vulnerable to both sudden transient sounds of still higher intensity (e.g. sound levels in the vicinity of 120 to 140 decibels and higher and to sustained excitation at sound levels from roughly 90 decibels and higher. Both disease and medical conditions such as diabetes (that produces a progressive neuropathy) can further contribute to gradual or acute hearing loss at the neurological level.
When hair cells die, they do not regenerate and hearing loss of this sort is thus cumulative over a lifetime. It is therefore a really good idea to wear ear protectors if, for example, you play an instrument in a marching band or a rock and roll band where your hearing is routinely exposed to 100 dB and up sounds. It is also a good reason not to play music too loudly when you are young, however pleasurable it might seem. One is, after all, very probably trading listening to very loud music at age seventeen against listening to music at all at age seventy. Hearing aids do not really fix the problem, although they can help restore enough function for somebody to get by.
However, it is quite possible that over the next few decades the bright and motivated physics students of today will help create the bioelectronic and/or stem cell replacements of key organs and nervous tissue that will relegate age-related deafness to the past. I would certainly wish, as I sit here typing this with eyes and ears that are gradually failing as I age, that whether or not it come in time for me, it comes in time to help you.