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A wire of uniform cross-section is stret...

A wire of uniform cross-section is stretched between two points `100cm` apart. The wire is fixed at one end and a weight is hung over a pulley at the other end. A weight of 9kg produces a fundamental frequency of `750Hz`.
(a) What is the velocity of the wave in wire?
(b) If the weight is reduced to `4kg`, what is the velocity of wave?

Text Solution

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The correct Answer is:
A, B, C
(a) `L=100cm`, `f_1=750Hz`
`v_1=2Lf_1=2xx100xx750`
`=150000cms^-1=1500ms^-1`
(b) `v_1=sqrt((T_1)/(mu))` and `v_2=sqrt((T_2)/(mu))`
`(v_2)/(v_1)=sqrt((T_2)/(T_1))`
:. `(v_2)/(1500)=sqrt((4)/(9))`
`:. v_2=1000ms^-1`
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