A vibrating stretched string resonates with a tuning fork of frequency 512 Hz when the length of the string is 0.5 m . The length of the string required to vibrate resonantly with a tuning fork of frequency 256 Hz would be ……… .

Options

A. 0.25 m
B. 0.75 m
C. `1.0` m
D. `2.0` m

Answer

C

Explanation

`v prop (1)/(L) implies (L_(2))/(L_(1)) = (v_(1))/(v_(2))` or `L_(2) = (v_(1))/(v_(2)) L_(1) = (512 xx 0.5)/(256) = 1.0` m