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A standing wave on a string fixed at both ends is described by y = (3 mm) sin(pi*x/15) sin(400*pi*t), where x is in cm and t is in seconds. The string vibrates in 4 loops. What is the speed of transverse waves along the string?

1. 60 m/s
2. 120 m/s
3. 30 m/s
4. 15 m/s

Correct answer: 60 m/s

Solution

Comparing with y = A sin(kx) sin(omega*t), we get k = pi/15 rad/cm and omega = 400*pi rad/s. The wave speed v = omega/k = 400*pi/(pi/15) = 6000 cm/s = 60 m/s. This speed is an intrinsic property of the string and is the same for the fundamental mode.

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