A wire under tension vibrates with a fundamental frequency of 600 Hz.If the length of the wire is doubled,the radius is halved and the wire is made to vibrate under one-ninth the tension.Then the fundamental frequency will become

Options

A. 200 Hz
B. 300 Hz
C. 600 Hz
D. 400 Hz

Answer

A

Explanation

The fundamental frequency of vibration is
`v=(1)/(2Lr)sqrt((T)/(pirho))`
Where
T=Tension in the wire
L=Length of the wire
r=Radius of the wire
`rho`=Density of material of the wire
`therefore (V_(1))/(v_(2))=(L_(2)/(L_(1)))(r_(2)/(r_(1)))sqrt((T_(1))/(T_(2))`
`therefore (v_(1))/(v_(2))=((2L_(1))/(L_(1)))(((1)/(2)r_(1))/(r_(1)))sqrt(T_(1)/(T_(1)//9))=2xx(1)/(2)xx3`
`(v_(1))/(v_(2))=3 `
or `v_(2)=(v_(1))/(3) =(600Hz)/(3)`=200Hz