One end of a horizontal string is attached to a tine of a mechanically driven tu

Question

One end of a horizontal string is attached to a tine of a mechanically driven tuning fork that vibrates at 220 Hz with constant amplitude. The string passes over a pulley, and a 1.20-kg mass hangs vertically from the other end of the string. The linear mass density of the string is 0.0180 kg/m a) What is the speed of the transverse wave on the string? b) What is the wavelength? c) By what factors will (i) the wave speed and (ii) the wavelength change if the hanging mass is doubled (increased by a factor of 2)?

Explanation / Answer

a) velocity = sqrt(tension/linear density)

= sqrt((1.20 kg * 9.8 m/s^2) / (0.0180 kg/m))

= 25.56 m/s
b) wavelength = velocity / frequency

= 25.56 m/s / 220 Hz

= 0.1161 m
c) Since tension would double, it would increase by a factor of sqrt(2).

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