A string is attached to a vibrator and a standing wave is set up by adjusting th

Question

A string is attached to a vibrator and a standing wave is set up by adjusting the frequency of oscillation. The mass per unit length of the string is 3.90x10^-4 kg/m. The string is driven by an 82.0 Hz oscillator. The velocity of the wave traveling back and forth on the string is 48.3 m/s. The string has a length, L. A mass, M, (including the hanger) hangs from the end of the string after it passes over the pulley.

What is the wavelength of the standing waves?

What is the length L of the string?

What is the mass M that gives this particular standing wave?

Explanation / Answer

velocity of sound in string = (tension/mass per unit length)^1/2

So, tension T = 0.91N

Also, Tension in string = Mg

Wavelength of the standing waves = speed / frequency = 48.3 / 82 = 0.5890m

From f= v/2L ; 82 = 48.3 / 2*L

So, the length L of the string = 0.29m

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