An object of density 2000kg-`m^(-3)` is hung from a thin light wire . The fundamental frequency of the transverse waves in the wire is 2009 Hz. If the object if immersed in water such that half of its volume is submerged, the the fundamental frequency of the transverse waves in the wire is

Options

A. 200Hz
B. 173.2Hz
C. 100Hz
D. 141.4 Hz

Answer

B

Explanation

Fundamental frequency, initially
`n_1 = 1/(2l)sqrt(T/mu)=(1)/(2l) sqrt(V_g (2000))/(mu)`
Fundamental frequency, finally
`n_2 = 1/(2l)sqrt((Vg(2000-(1000)/(2)))/(mu))`
(here we applied loss of weight due to upthrust )
`=1/(2l) sqrt((Vg xx 1500)/(mu))`
` rArr (n_1)/(n_2)= sqrt(2000/1500) = sqrt(4/3)`
`rArr n_2 = (n_1 xx sqrt(3))/(2)= 100 sqrt(3)Hz =173. 2 Hz`