A standing wave pattern is created on a string with mass density = 0.00035 kg/m

Question

A standing wave pattern is created on a string with mass density = 0.00035 kg/m . A wave generator with frequency f = 62 Hz is attached to one end of the string and the other end goes over a pulley and is connected to a mass (ignore the weight of the string between the pulley and mass). The distance between the generator and pulley is L = 0.59m . Initially the 3rd harmonic wave pattern is formed.
a) What is the wavelength of the wave? _______________m
b) What is the speed of the wave? ______________m/s
c) What is the tension in the string? ________________N
d) What is the mass hanging on the end of the string? ________________kg

e) Now the hanging mass is adjusted to create the 2nd harmonic. The frequency is held fixed at f = 62 Hz. What is the wavelength of the wave? ________________m
f) What is the speed of the wave? ______________m/s
g) What is the tension in the string? ________________N
h) What is the mass hanging on the end of the string? ________________kg

Explanation / Answer

The gravity force on the mass supplies the tension m . g = 0.155 m = 0.0158 kg ( 15.8 grams ) Increasing the mass will increase the tension, which will increase the velocity. With a fixed frequency this means that the wavelength must increase. The maximum wavelength possible is 1.1 m so the maximum speed ( to produce a coherent standing wave ) = 61 . 1.1 = 67.1 m/s 67.1 = v T / 0.00031 4502 . 0.00031 = T = 1.3957 N M (max) = T / g = 0.142 kg = 142 grams.

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