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.

A 60 cm long granite rod is fixed at its midpoint and then longitudina

1.	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.
Answer» (A) 5 kHz (B) `2.5 kHz` (C) `10 kHz` (D) `7.5kHz` SOLUTION :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`