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The note produced by a stretched string has a f... - JAMB Physics 1994 Question

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
correct option: b

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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