The note produced by a stretched string has a fundamental frequency of 400Hz. If the...

JAMB 1994

The note produced by a stretched string has a fundamental frequency of 400Hz. If the length of the string is doubled while the tension in the string is increased by a factor of 4, the frequency is

A. 200Hz
B. 400Hz
C. 800Hz
D. 1600Hz

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Correct Answer: Option B

Explanation

F = \(\frac {1}{2L}\) \(\sqrt\frac{T}{m}\)

T₂ = 4T₁ ; L₂ = 2L₁

\(\frac{2F_1L_1}{2F_2L_2}\) = \(\sqrt\frac{T_1}{T_2}\)

\(\frac{400\times L_1}{F \times L_1}\) = \(\sqrt\frac{T_1}{4T_1}\)

F = 400Hz

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