Question

The difference between the apparent frequency of a source of sound as perceived by the observer during its approach and recession is 2% of the frequency of the source. If the speed of sound in air is 300 ms^-1, then the velocity of the source is ______.

Options

• 1.5 ms^-1

• 12 ms^-1

• 6 ms^-1

• 3 ms^-1

Answer 1

The difference between the apparent frequency of a source of sound as perceived by the observer during its approach and recession is 2% of the frequency of the source. If the speed of sound in air is 300 ms^-1 , then the velocity of the source is 3 ms^-1.

Explanation:

The apparent frequency, when observer is approaching source is

n₁ = `((300 + "v")/ 300)` n

The apparent frequency, when observer is moving away from the source is

n₂ = `((300 - "v")/300)` n

According to given question,

n₁ − n₂ = `2/100` n

`therefore ((300 + "v")/300 - (300 - "v")/300) = 2/100`

`therefore 2"v" = 2 xx 3 Rightarrow "v"= 3 "m/s"`