A wire PQ has length 4.8 m and mass 0.06 kg . Another wire QR has length 2.56 m and mass 0.2 kg . Both wires have same radii and are joined as a single wire. This wire is under tension of 80 N . A wav

Question

A wire PQ has length 4.8 m and mass 0.06 kg . Another wire QR has length 2.56 m and mass 0.2 kg . Both wires have same radii and are joined as a single wire. This wire is under tension of 80 N . A wave pulse of amplitude 3.5 cm is sent along the wire PQ from end P . The time taken by the wave to reach the other end of single wire is (No power is dissipated during propagation)

TestHub · Accepted Answer

Mass per unit length for wire PQ , m PQ ​ = L M ​ = 4.8 0.06 ​ = 80 1 ​ kg / m Similarly for wire QR , m QR ​ = 2.56 0.2 ​ = 64 5 ​ kg / m ∴ Velocity of the wave in PQ wire: y = m PQ ​ T ​ ​ = 1/80 80 ​ ​ = 80 m / s ∴ Time taken to travel PQ wire, t = v d ​ = 80 4.8 ​ = 0.06 s Velocity of wave in QR wire, v ​ = m QR ​ T net ′ ​ ​ ​ = 5 ( 80 + 0.6 ) × 64 ​ ​ = 32.12 m / s ​ ∴ Time taken to travel QR wire, t = 32.12 2.56 ​ = 0.08 s So, total time taken will be: t = 0.06 + 0.08 = 0.14 s

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