All work needs to be shown and both bonus qn dproblem 4 need to be completed The
ID: 2299165 • Letter: A
Question
All work needs to be shown and both bonus qn dproblem 4 need to be completed
The phase velocity of seismic shear waves depends on two material properties: the mass density rho = Deltam/DeltaV of the medium, and a property called the shear modulus mu, which has units of pressure. Using dimensional analysis, what can you say about the phase velocity of shear waves? In 3.(d) you saw one way to read off the phase velocity from the expression for y(x, t). Depending on how y is written, reading off the phase velocity may not always be that obvious. For instance, we could have written the same wave as y(x, t) = ymexp[ - (x/x0)2 + 2xct/x02 - (ct/x0)2], which makes the right choice of g[x) much more obscure. Do you see a second method for determining the phase velocity, perhaps more directly related to the wave equation itself? Apply it to the Gaussian wave pulse and be patient with tedious derivatives.Explanation / Answer
First, what we think of as 'sound' really has two parts to it. Physical sound consists of waves in the air formed by the cause of the noise, whether it be speech or the clatter of dishes. Then, physiologically speaking, the sound is what is heard when the ear detects the sound wave and converts it into a message that the brain can understand. (Physiology deals with the normal functions and parts of organs.)
Sound waves are formed in a way that might surprise you: when air is pushed outward (as from a tree falling), it clumps together or compresses. When the air stops being pushed, there's a 'dead space' or decompressed area behind the clump, where there is little (or no) air. If air is pushed out at regular intervals, the clumps and dead spaces combine to form a longitudinal wave.
Longitudinal waves move along a line of travel through a series of compressions and decompressions. If you have a slinky, you can demonstrate what the movement of a sound wave looks like. Stretch out the slinky half way, and then give one end a hard push forward. A compression should form at that end of the slinky and move up the coil. Then, if it hits the other end hard enough, the motion will ripple back down the coil to the end that the movement started from.
Some sound waves have higher frequencies than others, resulting in higher pitch when the sound wave is transmitted to the brain via the ear. Frequency is the number of complete sound wave cycles that occurs in one second. In the same way, waves with a larger amplitude hit the eardrum with greater intensity, causing the brain to hear it as a louder sound. Amplitude is the pressure difference caused by the sound wave as it moves through the air.
Human ears can only hear sonic waves, ones that have a frequency between 20 and 20,000 hertz (Hz). Sound waves that have a lower frequency are called infrasonic, and waves which have a higher frequency are called ultrasonic. (Ultrasonic waves are the ones which are used in ultrasound imaging.)
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