Question

The difference between the apparent frequency of a stationary 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 observer is

Options

• 1.5 ms^–1

• 3 ms^–1

• 6 ms^–1

• 12 ms^–1

Answer 1

3 ms^–1 

Explanation:

The apparent frequency as the observer approaches the source is

n₁ = `((300 + v)/300)`n

When observer 1 moves away from the source, the apparent frequency is

n₂ = `((300 - v)/300)`n

According to the provided circumstance,

n₁ – n₂ = `2/100` n

∴ `(300 + v)/300 - (300 - v)/300 = 2/100`

∴ 2v = `2 xx 3` ⇒ 3 m/s