JAMB - Physics (1994 - No. 24)
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
200Hz
400Hz
800Hz
1600Hz
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
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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