Question

Q9

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, how far apart would the red dots be? m How far apart would the blue dots be? cm (b) In reality would adjacent dots in each set be far enough apart for you to easily measure their separation with a meterstick? Yes No (c) Suppose you repeated part (a) in water, where sound travels at 1480 m/s. How far apart would the red dots be? m How far apart would the blue dots be? cm Could you readily measure their separation with a meterstick? Yes No

Answer 1

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.