One end of a horizontal rope is attached to a prong of an electrically driven tu

Question

One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at a frequency 129 Hz . The other end passes over a pulley and supports a mass of 1.50 kg. The linear mass density of the rope is0.0510 kg/m . What is the speed of a transverse wave on the rope? What is the wavelength? What is the speed of a transverse wave on the rope if the mass were increased to 3.00 kg? What is the wavelength of a transverse wave on the rope if the mass were increased to 3.00 kg?

Explanation / Answer

A.

Speed of transverse wave is given by:

v = sqrt (T/u)

u = linear mass density = 0.0510 kg/m

T = m*g = 1.5*9.81

So,

v = sqrt (1.5*9.81/0.0510) = 16.986 = 17.0 m/sec

B.

wavelength = v/f

lambda = 17.0/129 = 0.132 m

C.

when mass = 3 kg

v = sqrt (3*9.81/0.0510) = 24.022 = 24.0 m/sec

D.

wavelength = v/f

lambda = 24.0/129 = 0.186 m

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