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By joining two wires PQ and QR, having l...

By joining two wires PQ and QR, having lengths 4.8 m and 2.56 m, having masses 0.06 kg and 0.2 kg having same radii of cross section, a single wire PQR is prepared. When this wire has a tension of 80 N, find time taken by a pulse produced at P to reach at R.

Text Solution

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Wave speed in wire PQ,
`v _(1) = sqrt ((T)/( mu _(1)) ) sqrt ((T )/( M _(1) // L _(1))) = sqrt ((T L _(1))/( M _(1))) = sqrt (( 80 xx 4.8 )/(0.06 ))= 80 (m)/(s)`
Similarly, wave speed in wire OQ,
`v _(2) = sqrt (( T )/(mu _(2))) = sqrt ((T)/( M _(2) // L _(2)))= sqrt ((T L _(2))/( M _(2))) = sqrt (( 80 xx 2.56)/( 0.2)) = 32 (m)/(s)`
Now, time taken by the wave to travel from P and Q,
`t = t _(1) + t _(2) = (L_(1))/( v _(1)) + (L _(2))/( v _(2)) = (4.8)/( 80) + (2.56)/(32)`
`=0.06 + 0.08 = 0.14 s `
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