Question

Two tuning forks with natural frequencies 340 Hz each move relative to a stationary observer. One fork moves away from the observer, while the other moves towards the observer at the same speed. The observer hears beats of frequency 3 Hz. Find the speed of the tuning forks.

• A. \(1.5\,\text{m/s}\)
• B. \(2\,\text{m/s}\)
• C. \(1\,\text{m/s}\)
• D. 2.5m/s

Hint:

When two identical sources move symmetrically: • Beat frequency arises due to Doppler shift. • Use difference of apparent frequencies. • Medium speed cancels out neatly.

Answer 1

The Correct Option is A

Step 1: Apparent frequencies heard by the observer are given by Doppler effect: f₁ = f(1 + (vₛ)/(v)), f₂ = f(1 - (vₛ)/(v)) where vₛ is speed of tuning fork and v = 340m/s.
Step 2: Beat frequency is the difference of apparent frequencies: |f₁ - f₂| = 2f(vₛ)/(v)
Step 3: Substituting given values: 3 = 2 × 340 × (vₛ)/(340) ⟹ 3 = 2vₛ vₛ = 1.5m/s