A speaker fixed to a moving platform moves toward a wall, emitting a steady soun

Question

A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 240 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 7.00 Hz ?

Take the speed of sound to be 344 m/s.

Question 2.A train is traveling at 30.0

m/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 Hz.

The speed of sound in air should be taken as 344 m/s.

What frequency fapproach is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it?

What frequency frecede is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?

Explanation / Answer

frequency of sound coming after reflection from the wall f1 = fo*v/(v-Vp)

frequency observed by the person on the platform = f2 = (f1*
(v+vp))/(v) = (fo*(v+vp))/(v-vp)

number of beats to be detected = 7

i.e = f2 - f1 = 7

(fo*(v+vp))/(v-vp) - fo*v/(v-Vp) = 7

(fo*vp)/(v-vp) = 7

(240*vp)/(344-vp) = 7

240*vp = 344*7 - 7*vp

247*vp = 2408

vp = 9.75 m/s   <----answer

-----------------------

Q2)

fapproach = (fo*(v+v2))/(v-v1)

fapproach = (262*(344+18))/(344-30) = 302.051 Hz   <-----answer

frcede = (fo*(v-v2))/(v+v1)

frecede = (262*(344-18))/(344+18) = 235.945 Hz <-----answer

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