Question:
what is the velocity of transverse waves traveling along a thin copper wire of length 50cm and mass of 1gram if it is stretched by a weight of 4kg
Answer:
Given
Mass of string, m = 1 gm = 1 * 10-3Kg
Length of the string, l = 50 cm = 50 * 10-2 m
The weight of 4Kg causes tension in the string
Hence, the Tension in string due to the weight of 4kg,
T = mg = 4 kg *9.8 = 39.2 N ----Eqn (1)
Velocity of the transverse wave v = ?
We know that velocity of a transverse wave on a string is given by, v = √(Tension/μ) where T is tension in string and μ is the mass per unit length
μ = mass/length = 1 * 10-3Kg / 50 * 10-2 = 1/500 kg/m ----------Eqn(2)
Substitute from Eqn (1) and Eqn (2) to get the velocity of transverse wave
v = √( 39.2/ (1/500) ) = √19600 = 140 m/sec
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