Audible Sound provided the amplitude is sufficiently great, the human ear can re

Question

Audible Sound provided the amplitude is sufficiently great, the human ear can respond to longitudinal waves over a range of frequencies from about 20.0 Hz to about 20.0 kHz.
(a) If you were to mark the beginning of each complete wave pattern with a red dot for the long-wavelength sound and a blue dot for the short-wavelength sound, bow far apart would the red dots be, and how far apart would the blue dots be?
(b) In reality would adjacent dots in each set be far enough apart for you to easily measure their separation with a meter stick?
(c) Suppose you repeated part (a) in water, where sound travels at 1480 m/s. How far apart would the dots be in each set? Could you readily measure their separation with a meterstick?

Explanation / Answer

I like to say, "What's new?" "c over lamda," to remember how frequency, nu, is related to the speed of a wave, c for light, and its wavelength, lamda. 20.0 Hz speed of sound at RT is 343 m/s so wavelength is lamda = speed/frequ = 343m/s / 20/s = 17m. The red dots would be 17m apart. 20,000 Hz lamda = 343m/s / 20,000/s = 0.01715 m = 1.7 cm (b) you would be able to measure the separation of the 20,000 Hz sound with a meter stick by counting ten from the first dot and then dividing the length by ten. You would rather have a tape measure to measure the red dot separation. (c) now the speed is much larger, so the wavelengths will be longer 20 Hz gives; lamda = 1480m/s / 20/s = 74m 20,000 Hz gives; lamda = 1480m/s / 20,000/s = 0.074m = 7.4 cm. This could be measured with a meter stick. Again, we could count off ten from the first dot and then divide the length by ten. 74m is hard to measure with a meter stick.

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