A tuning fork is exactly in resonance with the fundamental mode of a sonometer wire when the wire tension is 16 N. The vibrating length and linear density are kept unchanged, and the tension is increased to 36 N. The wire then produces 90 beats per second with the same tuning fork. What is the tuning-fork frequency?
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Question

A tuning fork is exactly in resonance with the fundamental mode of a sonometer wire when the wire tension is 16 N. The vibrating length and linear density are kept unchanged, and the tension is increased to 36 N. The wire then produces 90 beats per second with the same tuning fork. What is the tuning-fork frequency?

Options

G1 Physics · Accepted Answer

For a sonometer wire with fixed length and linear density, f ∝ √T. Initially the string is in resonance with the fork, so let their common frequency be f₀. After the tension changes, fₛ₂/f₀ = √(36/16) = 3/2. Thus, fₛ₂ = 3f₀/2. The beat frequency is 3f₀/2−f₀ = f₀/2. Given, f₀/2 = 90. Therefore, f₀ = 180 Hz. Correct option: C.