Power required to generate waves

[gleeson.tim]

1.
Determine the speed of transverse waves on
a string under a tension of 73 N if the string
has a length of 2.1 m and a mass of 5.9 g
Answer= 161.1925893 m/s

I have a problem with the second part of the question:
Calculate the power required to generate
these waves if they have a wavelength of 29 cm
and an amplitude of 7.3 cm. Answer in units
of kW.


2. Velocity= Square Root [Tension/(mass/length)]

Energy= 2 pi^2 mf^2 A^2
A-amplitude
m-mass
f- frequency

Power= Energy/time

3. I found the frequency by taking the velocity/wavelength and then found the energy using the above equation. I tried to find a value for time by taking the inverse of the frequency (period) and then plugging the values into P=E/t, but was not correct

 

[LowlyPion]

P = ΔE / Δt

From your Energy equation.

E = 1/2*μ*λ*ω²A²

μ = .0059/2.1 = .00281

And your t can be found by λ/ν

making it

P = 1/2*μ*ν*ω²A²

What did you calculate?

 

[gleeson.tim]

Thanks, that worked. It ended up being 14.72 kW

 

[greenorb]

Hey I have a problem similar to this one. What is the value for the lowercase omega (w)?
I looked everywhere but I don't know how to find it

 

[rwisz]

. I would need more information about the system to accurately calculate the power required to generate these waves. Some important factors to consider would be the type of wave being generated (e.g. transverse, longitudinal), the medium through which the wave is traveling, and any external forces or factors affecting the system. Additionally, the question does not specify the time frame over which the power is being calculated, which could also impact the final result. Without this information, it is not possible to accurately determine the power required to generate these waves.