Power required to generate waves

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SUMMARY

The discussion focuses on calculating the power required to generate transverse waves on a string under a tension of 73 N, with a length of 2.1 m and mass of 5.9 g. The speed of the waves is determined to be approximately 161 m/s. The power calculation involves using the formula Power = Energy/time, where Energy is derived from the equation Energy = 2π²mf²A², with the amplitude set at 7.3 cm and wavelength at 29 cm. The correct approach emphasizes using significant figures, suggesting that the final speed should be reported as 160 m/s or 161 m/s.

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  • Understanding of wave mechanics and transverse waves
  • Familiarity with the tension, mass, and length of strings
  • Knowledge of significant figures in scientific calculations
  • Ability to convert units, specifically from centimeters to meters
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  • Learn how to calculate wave frequency from velocity and wavelength
  • Study the concept of energy in wave mechanics, specifically Energy = 2π²mf²A²
  • Explore the significance of significant figures in scientific reporting
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Students and professionals in physics, particularly those studying wave mechanics, as well as engineers and educators involved in teaching concepts related to wave dynamics and energy calculations.

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!
 

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