Power required to generate waves

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The discussion focuses on calculating the speed of transverse waves on a string with a tension of 73 N, resulting in a speed of approximately 161 m/s. The second part involves calculating the power required to generate these waves, given a wavelength of 29 cm and an amplitude of 7.3 cm. The formula for velocity is derived from the tension and mass per length, while energy is calculated using the amplitude and frequency. There is a clarification that the mass in the energy equation refers to the mass of one wavelength of the medium. Additionally, it is emphasized that results should be rounded to two significant digits for accuracy.
gleeson.tim
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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
 
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The "mass" of this equation refers to the mass of the medium through which the wave travels in one cycle. That is, the mass of "one wavelength" of the medium.

Don't forget to convert distances to meters.

And by the way, your answer for the speed is correct, but please...

There are only two digits going into the equations, so there should only be two significant digits coming out. The answer ought to be 160 m/s, and few would complain if you put, 161 m/s, but you should NOT put in all the digits your calculator gave you!
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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