A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 235 Hz. A person on the platform right next to the speaker detects the sound waves reflected off the wall and those emitted by the speaker. How fast should the platform move, vp, for the person to detect a beat frequency of 4.00 Hz? Take the speed of sound to be 344 m/s.

2.9 m/s

Explanation:

The frequency of the beat is 4 Hz

The relative Doppler frequency is 235 + 4 = 239 Hz

We would be solving this question, using the formula for Doppler's effect

f(d) = f(v+vr)/(v-vs), where

F = 235 Hz

F(d) = 239 Hz

v = 344 m/s and vr = vs

239 = 235 (344 + vr) / (344 - vr)

239 ( 344 - vr) = 235 (344 + vr)

82216 - 239 vr = 80849 + 235 vr

82216 - 80849 = 235 vr + 239 vr

1376 = 474 vr

vr = 1376/474

vr = 2.9 m/s

Thus the speed the platform should move is 2.9 m/s

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)