Two tuning forks A and B lying on opposite sides of observer ‘O’ and of natural frequency 85 Hz move with velocity 10 m s⁻¹ relative to stationary observer O. Fork A moves away from the observer while the fork B moves towards him. A wind with a speed 10 m s⁻¹ is blowing in the direction of motion of fork A. Find the beat frequency measured by the observer in Hz. (Take speed of sound in air as 340 m s⁻¹)
Physics · Wave Motion
JEE Mains Practice

Question

Two tuning forks A and B lying on opposite sides of observer ‘O’ and of natural frequency 85 Hz move with velocity 10 m s⁻¹ relative to stationary observer O. Fork A moves away from the observer while the fork B moves towards him. A wind with a speed 10 m s⁻¹ is blowing in the direction of motion of fork A. Find the beat frequency measured by the observer in Hz. (Take speed of sound in air as 340 m s⁻¹)

Physics · Wave Motion

G1 Physics · Accepted Answer

Step 1: Work in the air frame because wind is present. Fork A and fork B each have 85 Hz, but their source velocities relative to the air are different because the wind is 10 m s⁻¹ in the direction of A. Step 2: Apply f′ = f(v+vₒ)/(v−vₛ) separately for the two approaching/receding cases, using velocities relative to air. Step 3: The two received frequencies differ by 5 Hz. Final answer: 5.