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 Answer: Option B
Explanation
F = (frac {1}{2L}) (sqrtfrac{T}{m})
T2 = 4T1 ; L2 = 2L1
(frac{2F_1L_1}{2F_2L_2}) = (sqrtfrac{T_1}{T_2})
(frac{400times L_1}{F times L_1}) = (sqrtfrac{T_1}{4T_1})
F = 400Hz