Question

3.
Two sound source S, and S, have the frequencies
224 Hz and 220 Hz and are situated at some
distance. An observer is moving on the line joining
the sources. If the observer does not hear a beat,
his speed will be- (given velocity of sound
v = 333 m/s) (in m/s)​

Answer 1

His speed will be 2 m/s

Explanation:

Actual frequency of the first source is 224 Hz

Actual frequency  of the second source is 220 Hz

Apparent frequency of the sound when source is at rest and listener is moving is at rest.

f = v−v1 / v × f0

v is the velocity of sound.

v1 is the velocity of listener.

for source s1, listner is moving towards the s1

f1 = v+v / v×224

for source s2 , listner is moving away from the source

f2 =v−v / v×220

for no beat frequency  f1 −f2 = 0

v+v1 / v×224 −v−v1 / v× 220 = 0

v+v1 / v × 224 = v−v1 / v× 220

2v1 = 4 m/s = 2m/s

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