Estimation of frequency of a wave forming a standing wave represented by `y = A sin kx cos t` can be done if the speed and wavelength are known using `speed = "Frequency" xx "wavelength"` . Speed of motion depends on the medium properties namely tension in string and mass per unit length of string . A string may vibrate with different frequencies . The corresponding wavelength should be related to the length of the string by a whole number for a string fixed at both ends . Answer the following questions:
A string fixed at both ends having a third overtone frequency of `200 Hz` while carrying a wave at a speed of `30 ms^(-1)` has a length of

Options

A. `30 m`
B. `22.5 cm`
C. `30 cm`
D. `10.25 cm`

Answer

C

Explanation

Third overtone ( fourth harmonic) frequency in string is
`( 4 v)/( 2 l) = 200 Hz`
` l = ( 4v)/(400) = (v)/(100) = (30)/(100) 0.30 m = 30 cm`