# 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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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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Step 1 help_outlineImage TranscriptioncloseEach 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 fullscreen
Step 2 help_outlineImage TranscriptioncloseEquate 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 fullscreen

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### Wave Motion 