A tuning fork resonates with the fundamental mode of a sonometer wire when the wire tension is 16 N. The tension is increased to 36 N while length and linear density remain unchanged, and the wire then gives 90 beats per second with the same fork. If the tuning-fork frequency is N Hz, find N.
Physics · Wave Motion · Beats, Loudness, Pitch and Characteristics of Sound
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Question

A tuning fork resonates with the fundamental mode of a sonometer wire when the wire tension is 16 N. The tension is increased to 36 N while length and linear density remain unchanged, and the wire then gives 90 beats per second with the same fork. If the tuning-fork frequency is N Hz, find N.

Physics · Wave Motion · Beats, Loudness, Pitch and Characteristics of Sound

G1 Physics · Accepted Answer

For fixed length and linear density, f ∝ √T. Hence, f₂/f₁ = √(36/16) = 3/2. Initially the string frequency equals the fork frequency N. After changing tension, fₛ₂ = 3N/2. The beat frequency is 3N/2−N = N/2. Given, N/2 = 90. Thus, N = 180.