Question

A source and an observer move away from each other with a velocity of 10m/s with respect to ground.If the observer finds the frequency of sound coming from the source as 1950 Hz,then actual frequency of the source is (velocity of sound in airt =340m/s):a)2486Hz b)2132Hz c)2068Hz d)1950Hz.

Answer 1

Answer on Question #38032, Physics, Other

Question:

A source and an observer move away from each other with a velocity of 10m/s with respect to ground. If the observer finds the frequency of sound coming from the source as 1950 Hz, then actual frequency of the source is (velocity of sound in airt =340m/s):

a)2486Hz

b)2132Hz

c)2068Hz

d)1950Hz.

Answer:

In classical physics the relationship between observed frequency $f$ and emitted $f_0$ is given by:

$$f = f_0 \frac{c + v_r}{c + v_s}$$

where

$c$ is the velocity of waves in the medium;

$v_r$ is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction);

$v_s$ is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).

Therefore:

$$f_0 = f \frac{c + v_s}{c + v_r} = 1950 \frac{340 + 10}{340 - 10} = 2068 \text{ Hz}$$

Answer: c)2068Hz