A wire stretched between two rigid supports vibrates in tits fndamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 xx 10 ^(-2) kg andits inear mass density is 4.0 xx 10 ^(-2) kg m ^(-1). What is (a) the speed oa a transverse wave on the string, and (b) the tension in the string ?

A wire stretched between two rigid supports vibrates in tits fndamenta

1.	A wire stretched between two rigid supports vibrates in tits fndamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 xx 10 ^(-2) kg andits inear mass density is 4.0 xx 10 ^(-2) kg m ^(-1). What is (a) the speed oa a transverse wave on the string, and (b) the tension in the string ?
Answer» Solution :(a) Fundamental frequency of stationary wave, `f _(1) = (V)/(2L) implies f _(1) =(v mu)/(2 xx M)` `(because mu = (M)/(L) implies L = (M)/(mu)) ` `THEREFORE v =(2f _(1) M )/( mu) = (2 xx 45 xx 0.035)/(0.04) = 78.75 (m)/(s)` (b) Wave speed of transverse wave, `v = sqrt ((T)/(mu))` `therefore v ^(2) = (T)/(mu) implies T = muv ^(2)` `therefore T = (0.04) (78,75)^(2) = 248.1 N`