Question

Two tuning forks \(A\) and \(B\) are sounded together giving rise to 8 beats in 2 s. When fork \(A\) is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork \(B\) is \(380\ \text{Hz}\), find the original frequency of tuning fork \(A\). Given: \[ f_B = 380\ \text{Hz} \]

Hint:

Adding wax to a tuning fork always decreases its frequency due to increase in effective mass.

Answer 1

Correct Answer: 384

Concept: Beat frequency is given by: \[ f_b = |f_A - f_B| \]
Step 1: Initial beat frequency \[ \text{Beats per second}=\frac{8}{2}=4 \] \[ |f_A-380|=4 \] \[ f_A=384\ \text{Hz} \quad \text{or} \quad 376\ \text{Hz} \]
Step 2: Effect of loading with wax Loading a tuning fork decreases its frequency. Since beat frequency reduces after loading, the difference between frequencies decreases. Hence, initially: \[ f_A>f_B \] So, \[ f_A = 384\ \text{Hz} \] Final Answer: \[ \boxed{384\ \text{Hz}} \]