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.

By joining two wires PQ and QR, having lengths 4.8 m and 2.56 m, havin

1.	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.
Answer» Solution :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 `