The maximum tension in the string is 102.2 N
Explanation:
The speed of the standing wave in the guitar can be found by using the wave equation:
[tex]v=f \lambda[/tex]
where
f is the frequency of the wave in the string
[tex]\lambda[/tex] is the wavelength
Here we know that:
[tex]f=82.41 Hz[/tex]
The wavelength of the standing wave in a string is twice the length of the string, so:
[tex]\lambda = 2 L = 2(0.69)=1.38 m[/tex]
Therefore, the speed is
[tex]v=(82.41)(1.38)=113.7 m/s[/tex]
The speed of the wave is also related to the tension in the string by the formula
[tex]v=\sqrt{\frac{T}{\mu}}[/tex]
where
T is the tension in the string
[tex]\mu[/tex] is the linear density of the string
Here we know that
[tex]\mu = 0.0079 kg/m[/tex]
So, we can re-arrange the equation to find T:
[tex]T=\mu v^2 = (0.0079)(113.7)^2=102.2 N[/tex]
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The proper tension the string is mathematically given as
T=102.2 N
Question Parameter(s):
The low E string has a linear density of rho = 0.0079 kg/m
Randomized Variables L 0.73 m p 0.0059 kg/m A 50%
Generally, the equation for the speed is mathematically given as
v=f *lambda
Where
lambda = 2 L
lambda= 2(0.69)
lambda=1.38 m
Therefore
v=(82.41)(1.38)
v=113.7 m/s
In conclusion, speed of the wave is
[tex]v=\sqrt{\frac{T}{\mu}}[/tex]
T=u*v^2
T= (0.0079)(113.7)^2
T=102.2 N
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