A 60 cm long granite rod is fixed at its midpoint and then longitudinal waves are set up in it. Find fundamental frequency of these waves. Density of granite is `2.7 xx 10^(3)` kg/m3 and its Young modulus is `9.27 xx 10 ^(10) Pa.`

Options

A. (A) 5 kHz
B. (B) `2.5 kHz`
C. (C) `10 kHz`
D. (D) `7.5kHz`

Answer

A

Explanation

Here speed od longitudinal wave, `v - sqrt ((Y)/(rho ))`
`therefore v = sqrt (( 9.27 xx 10 ^(10))/( 2.7 xx 10 ^(3))) = 5860 (m)/(s)`
Now, `v =f _(1) lamda_(1)`
(Where `f _(1)` = fundamental frequency)
`therefore v = f _(1) (2L) (because lamda _(n) = (2L)/(n ) and ` here `n =1 )`
`therefore f _(1) = (v)/(2L) = (5860)/(2 xx 0.6) = 4880 Hz ~~5 kHz`