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» <html><body><p></p>Solution :(a) Fundamental frequency of stationary wave, <br/> `f _(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) = (<a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/2l-300409" style="font-weight:bold;" target="_blank" title="Click to know more about 2L">2L</a>) implies f _(1) =(v mu)/(2 xx M)` <br/> `(because mu = (M)/(L) implies L = (M)/(mu)) ` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> v =(2f _(1) M )/( mu) = (2 xx 45 xx 0.035)/(0.04) = 78.75 (m)/(s)` <br/> (b) Wave speed of transverse wave, <br/> `v = sqrt ((T)/(mu))` <br/> `therefore v ^(2) = (T)/(mu) implies T = muv ^(2)` <br/> `therefore T = (0.04) (78,75)^(2) = 248.1 N`</body></html>