A string is attached to a vibrator as shown, and a standing wave is set up by ad
ID: 1787971 • Letter: A
Question
A string is attached to a vibrator as shown, and a standing wave is set up by adjusting the frequency of oscillation. The mass per unit length of the string is 4.90*10^- 4 kg/m. The string is driven by a 65.0 Hz oscillator. The velocity of the wave traveling back and forth on the string is 68.2 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. Assume the two ends are nodes of the standing wave.
What is the wavelength of the standing wave? What is the tension in string? What is the length of the string? What is the mass that gives the particular standing wave?
Explanation / Answer
speed v = lambda*f
wavelength , lambda = v/f = 68.2/65 = 1.05 m
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speed of wave in string v = sqrt(T/u)
T = tension force
u = mass per unit length
T = v^2*u = 68.2^2*4.9*10^-4
Tension = 2.28 N
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In fundamental mode of vibration
lambda = 2L
L = lambda/2 = 1.05/2 = 0.525 m
============================
mass = u*L
mass m = 4.9*10^-4*0.525
m = 0.000257 kg
m = 0.257 grams
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