Answer:
200 Hz.
Explanation:
given,
Length of the string,L = 4.29 m
Mass of the string,m = 228 g
Tension of the string,T = 31.1 N
frequency of travelling, f = ?
Amplitude of the wave,A = 6.83 mm
Average Power,P = 47.1 W.
we know,
[tex]P_{avg}=\dfrac{1}{2}\mu v\omega^2 A^2[/tex]
we know,
[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]
[tex]\omega = 2\pi f[/tex]
[tex]\mu = \dfrac{M}{l}=\dfrac{0.228}{4.29}= 0.05315\ kg/m[/tex]
inserting all the values
[tex]P_{avg}=\dfrac{1}{2}\times\sqrt{\mu T}\times (2\pi f)^2 A^2[/tex]
[tex]47.1=\dfrac{1}{2}\times\sqrt{31.1\times 0.05315}\times (2\pi f)^2\times A^2[/tex]
[tex]f=\sqrt{\dfrac{47.1\times 2}{\sqrt{31.1\times 0.05315}\times 0.00683^2\times4\times \pi^2}}[/tex]
f = 199.46 Hz
Hence, the frequency of wave is equal to 200 Hz.
