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
[tex]\lambda = 2 L[/tex]
where
[tex]\lambda[/tex] 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
[tex]\lambda=2(0.8)=1.6 m[/tex]
2)
The speed of a wave is calculated through the wave equation:
[tex]v=f\lambda[/tex]
where
f is the frequency
[tex]\lambda[/tex] is the wavelength
For the standing wave on this string, the fundamental frequency is
[tex]f=65.4 Hz[/tex]
while the wavelength is
[tex]\lambda=1.6 m[/tex]
Therefore, the speed of the wave is
[tex]v=(65.4)(1.6)=104.6 m/s[/tex]
3)
The speed of the wave is related to the tension in the string by
[tex]v=\sqrt{\frac{T}{\mu}}[/tex]
where
v is the speed
T is the tension
[tex]\mu[/tex] is the linear density of the string
For this string,
v = 104.6 m/s
[tex]\mu=1.56\cdot 10^{-2} kg/m[/tex]
Therefore, the tension in the string is
[tex]T=\mu v^2 = (1.56\cdot 10^{-2})(104.6)^2=170.7 N[/tex]
Learn more about waves:
brainly.com/question/5354733
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