# A string of length L = 2.9 m and mass m = 0.095 kg is fixed between tw

Mary Buchanan 2021-12-18 Answered
A string of length L = 2.9 m and mass m = 0.095 kg is fixed between two stationary points, and when the string is plucked a transverse wave of frequency f = 84 Hz is generated.
Part A: What is the strings linear density, $\rho$, in kilograms per meter?
Part B: If the wavelength is 10.0 cm, which harmonic is this, counting the fundamental as 1?
Part C: For the case described in Part (b), what is the tension in N?
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Travis Hicks
Given that the length of the string is 2.9m, and a mass of 0.095kg is fixed between the two stationary points. The frequency of the transverse wave is f = 84Hz.
Write the expression for linear mass density.
$\rho =\frac{M}{L}$
$=\frac{\left(0.095kg\right)}{2.9m}$
$=0.0327k\frac{g}{m}$
a) The linear mass density is $0.0327k\frac{g}{m}$

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Annie Gonzalez
Write the relation between the length of the string and number of loop.
$L=N\frac{\lambda }{2}$
$N=\frac{2L}{\lambda }$
$=\frac{2\left(2.9m\right)}{0.10m}$
= 58
The harmonic of the string wave is 58.

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nick1337

Write the expression for frequency.
$f=\frac{Nv}{2L}$
$v=\frac{2Lf}{N}$
$P=\frac{2\left(2.9m\right)\left(84Hz\right)}{58}$
$=8.4m/s$
The velocity can also be written as
$v=\sqrt{\frac{T}{\rho }}$
$T={v}^{2}\rho$
$=\left(8.4m/s{\right)}^{2}\left(0.0327kg/m\right)$
$=2.307N$
c) The tension is 2.307 N.

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