A musical note on a piano has a frequency of 40 Hz. If the tension in the 2-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?
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Expert's answer
2021-04-13T06:28:29-0400
Explanations & Calculations
Since a half of the wavelength is contained in the length of the wire as it make a stationary wave we can write if the length of the wire is l and the wavelength is λ,
2λ=l→λ=2l
As by now the wavelength is known we can apply the common equation v=fλ for the stationary wave generated on the wire,
v=40×2l=40×2×2m=160ms−1
Then, according to the equation for the speed of a wave on a wire as,
v=m′T→MTl
where m′ is the linear density of the wire whose total mass is M and the length is l.
Finally combining altogether yield the needed answer,
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