A tuning fork generates 4 beats per second when sounded with another tuning fork having a frequency of 256 Hz . When the first tuning fork is loaded with a small amount of wax, the beat frequency increases to 6 per second. Determine the original frequency of the first tuning fork.

Step-by-step solution

Let the frequency of the first tuning fork be n₁ and the second be n₂ = 256 Hz . The initial beat frequency is 4 Hz . n₁ = n₂ 4 = 256 4 n₁ = 260 Hz or 252 Hz When the first tuning fork is loaded with wax, its frequency decreases. If n₁ = 260 Hz , a small decrease in frequency would initially decrease the beat frequency (for example, to 259 Hz , giving 3 beats). If n₁ = 252 Hz , a small decrease in frequency would increase the beat frequency (for example, to 250 Hz , giving 6 beats). Since the beat frequency increas