1) Wavelength of the wave: 1.6 m
2) Speed of the wave: 104.6 m/s
3) Tension in the string: 170.7 N
Explanation:
1)
For the standing waves on a string, the wavelength of the wave is related to the length of the string by
![\lambda = 2 L](https://tex.z-dn.net/?f=%5Clambda%20%3D%202%20L)
where
is the wavelength
L is the length of the string
For the string in this problem.
L = 0.8 m is its length (I assume there is a mistake in the text, since 0.08 m is not a realistic value for the length of the string)
Therefore, the wavelength of the wave on the string is
![\lambda=2(0.8)=1.6 m](https://tex.z-dn.net/?f=%5Clambda%3D2%280.8%29%3D1.6%20m)
2)
The speed of a wave is calculated through the wave equation:
![v=f\lambda](https://tex.z-dn.net/?f=v%3Df%5Clambda)
where
f is the frequency
is the wavelength
For the standing wave on this string, the fundamental frequency is
![f=65.4 Hz](https://tex.z-dn.net/?f=f%3D65.4%20Hz)
while the wavelength is
![\lambda=1.6 m](https://tex.z-dn.net/?f=%5Clambda%3D1.6%20m)
Therefore, the speed of the wave is
![v=(65.4)(1.6)=104.6 m/s](https://tex.z-dn.net/?f=v%3D%2865.4%29%281.6%29%3D104.6%20m%2Fs)
3)
The speed of the wave is related to the tension in the string by
![v=\sqrt{\frac{T}{\mu}}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7BT%7D%7B%5Cmu%7D%7D)
where
v is the speed
T is the tension
is the linear density of the string
For this string,
v = 104.6 m/s
![\mu=1.56\cdot 10^{-2} kg/m](https://tex.z-dn.net/?f=%5Cmu%3D1.56%5Ccdot%2010%5E%7B-2%7D%20kg%2Fm)
Therefore, the tension in the string is
![T=\mu v^2 = (1.56\cdot 10^{-2})(104.6)^2=170.7 N](https://tex.z-dn.net/?f=T%3D%5Cmu%20v%5E2%20%3D%20%281.56%5Ccdot%2010%5E%7B-2%7D%29%28104.6%29%5E2%3D170.7%20N)
Learn more about waves:
brainly.com/question/5354733
brainly.com/question/9077368
#LearnwithBrainly