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 with 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. \(2.5 \text{ m/s}\)

Hint:

For beats with moving sources: \[ f_{\text{beat}} = |f_1 - f_2| \] Use Doppler formula carefully for approaching and receding sources.

Answer 1

The Correct Option is A

Step 1: Apparent frequencies due to Doppler effect: \[ f_1 = f\left(\frac{v}{v+u}\right), \quad f_2 = f\left(\frac{v}{v-u}\right) \]
Step 2: Beat frequency: \[ |f_2 - f_1| = 3 \]
Step 3: Substituting \(f=340\) Hz and speed of sound \(v=340\) m/s: \[ 340\left(\frac{340}{340-u} - \frac{340}{340+u}\right) = 3 \]
Step 4: Solving: \[ u = 1.5 \text{ m/s} \]