Question

A woman stands at rest in front of a large, smooth wall. She holds a vibrating tuning fork of frequency Initial: fo directly in front of her (between her and the wall).
(a) The woman now runs toward the wall with speed Pw, She detects beats due to the interference between the sound waves reaching her directly from the fork

Note: If the beat frequency is too large, the woman may have to use some instrumentation other than her e reaching her after being reflected from the wall. How many beats per second will she detect?

Answer 1

Answer:

(a) $f_{o}*\frac{2P_{w} }{v - P_{w} }$

(b) $f_{o}*\frac{2P_{w} }{v + P_{w} }$

Explanation:

(a) In the given problem, the turning fork has a frequency of $f_{o}$. Then, a woman runs toward the wall with a speed of $P_{w}$. From the principle of light reflection, the reflection of the sound from the fork reach the woman at a speed of v. Thus, the beat frequency is:

$f_{o}*\frac{2P_{w} }{v - P_{w} }$

(b) In this part, the woman moves away from the water which is in contrast to part (a). Thus the beat frequency is:

$f_{o}*\frac{2P_{w} }{v + P_{w} }$