A stationary 492 Hz source sends sound toward a large car approaching at 2 m s⁻¹. The reflected sound returns to the source and interferes with the original. Find the beat frequency. Take sound speed = 330 m s⁻¹.
Physics · Wave Motion
JEE Advanced 2017

Question

A stationary 492 Hz source sends sound toward a large car approaching at 2 m s⁻¹. The reflected sound returns to the source and interferes with the original. Find the beat frequency. Take sound speed = 330 m s⁻¹.

Physics · Wave Motion

JEE Advanced 2017

G1 Physics · Accepted Answer

Step 1: The car first acts as a moving observer: f₁=f₀(v+u)/v. It then reflects this frequency as a moving source: fᵣ=f₁·v/(v−u)=f₀(v+u)/(v−u). Step 2: Beat frequency = fᵣ−f₀ = f₀[2u/(v−u)]. With f₀=492, u=2 and v=330, this is 6 Hz.