Question
Asked Nov 9, 2019
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When a string that is 2m long is connected between two supports and vibrated at 176 Hz it is observed to produce 8 antinodes. If the tension on the string is 77.5 N what would the total mass of the string be?
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Expert Answer

Step 1
Each wavelength will have two antinodes. Since there are eight antinodes, 2m length is equal to
four times the wavelength. Thus, the wavelength is
2 m
4
=0.5 m
Here, A is the wavelength.
The wave equation is,
v=2f
Here, v is the speed of the wave and f is the frequency of the wave
The speed of propagation of wave in a string is given by
1 T
2L
Here, L is the length of the tube, T is the tension in the string and u is the linear mass density
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Image Transcriptionclose

Each wavelength will have two antinodes. Since there are eight antinodes, 2m length is equal to four times the wavelength. Thus, the wavelength is 2 m 4 =0.5 m Here, A is the wavelength. The wave equation is, v=2f Here, v is the speed of the wave and f is the frequency of the wave The speed of propagation of wave in a string is given by 1 T 2L Here, L is the length of the tube, T is the tension in the string and u is the linear mass density

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Step 2
Equate the above two equations.
T
1
2LV
2Laf=
т
Т
=1
4L2
The equation for the linear mass density is given by
т
= 1
Here, m is the mass of the string.
Thus
L
L 4
т
m=
4LA
help_outline

Image Transcriptionclose

Equate the above two equations. T 1 2LV 2Laf= т Т =1 4L2 The equation for the linear mass density is given by т = 1 Here, m is the mass of the string. Thus L L 4 т m= 4LA

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Physics

Wave Motion

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