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

 

[Chi Meson]

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!

 

[nlightner]

. Can you provide guidance on how to approach this problem?

I understand your confusion with the second part of the question. Calculating the power required to generate waves involves understanding the relationship between energy, frequency, and time. In this case, we know the wavelength and amplitude of the waves, but we need to find the frequency and period to accurately calculate the power required.

To find the frequency, we can use the equation f = v/λ, where f is frequency, v is velocity, and λ is wavelength. Using the velocity value you found in your answer to the first part of the question (161.1925893 m/s), we can calculate the frequency to be approximately 555.5 Hz.

Next, we can find the period by taking the inverse of the frequency, which is 1/f = 1/555.5 Hz = 0.0018018 seconds.

Now, we can calculate the energy of the waves using the equation E = 2π^2mf^2A^2, where m is mass, f is frequency, and A is amplitude. Plugging in the given values, we get E = 2π^2(0.0059 kg)(555.5 Hz)^2(0.073 m)^2 = 0.0009458 J.

Finally, we can calculate the power required using the equation P = E/t, where P is power, E is energy, and t is time. Plugging in the values we found, we get P = 0.0009458 J/0.0018018 s = 0.525 W.

To convert this to kW, we divide by 1000, giving us a final answer of 0.000525 kW.

I hope this helps guide you in approaching this problem. Remember to always use the correct equations and units when solving scientific problems.