Wave power on string question

In summary, a 6.00m segment of a long string with a mass of 180g contains four complete waves, vibrating sinusoidally with a frequency of 50.0hz and a peak-to-valley distance of 15.0cm. The function describing this wave traveling in the positive x direction is v = (L * f)/4. The power being supplied to the string is given by the equation P = 1/2*u*w^2*A^2*v, where v = (L * f)/16.
  • #1
industry86
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--It is found that a 6.00m segment of a long string contains four complete waves and has a mass of 180g. The string is vibrating sinusoidally with a frequency of 50.0hz and a peak-to-valley distance of 15.0cm. (a) Write the function that describes this wave traveling in the positive x direction. (b) Determine the power being supplied to the string.--

Ok, I determined that w=2*pi*50hz=314 rad/s. k= (2*pi)/wave length=4.19rad/m (assuming that the 6m long segment with 4 equal length waves would give me a 1.5m wave length)

so i can answer (a), although having the A=6.00m is starting to bug me since the string is actually a lot longer that the segment experiencing the waves.

(b), is killin me though. I figure all i have to use is the P=1/2*u*w^2*A^2*v bit, but i can't seem to figure out v.
v=wave length*freq.
v=w/k
v=sqrt(period/u)

but if I use what I have determined previously, the first two equations come up with teh same answer, but the third one doesn't. the first 2 are 75m/s, the third is something like .81m/s. This makes me think that either my period, which I determined is .02s, is wrong, or something else is fundamentally wrong. And am I even using the right equation for the power?

---------------------------------------------
Um, since I don't know how to delete this post, I'll just correct myself here.

v=wavelength*freq
v=w/k
v=sqrt(TENSION!...not period/u)

please ignore this now
 
Last edited:
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  • #2
*I'm just posting this despite the 6 year lapse for anyone else who will use this as future reference*

from part A, we know that
v = L/t
t = 1/f -> four complete waves -> 4/f
so v = (L * f)/4

however, for part B, in order to find the power throughout the string, we have to take the velocity from A and divide it by 4. so,
v = (L * f)/16

and yes, that was the right power equation.
 

1. How does wave power on a string work?

Wave power on a string is a form of wave energy conversion, where the kinetic energy of ocean waves is harnessed and converted into electrical energy. This is achieved by attaching a string to a floating buoy, which moves up and down with the waves, generating tension on the string. This tension is then used to turn a generator, producing electricity.

2. What are the advantages of using wave power on a string?

One of the main advantages of wave power on a string is that it is a renewable source of energy, as ocean waves are constantly generated by the wind. It is also a clean source of energy, as it does not produce any carbon emissions. Additionally, wave power on a string has a low visual and environmental impact compared to other forms of renewable energy, such as wind or solar power.

3. Are there any limitations to wave power on a string?

While wave power on a string has many benefits, there are some limitations to its use. One of the main challenges is the unpredictable nature of ocean waves, which can vary in size, frequency, and direction. This makes it difficult to consistently harness wave energy and may require advanced technology to adapt to changing wave conditions. The cost of installation and maintenance is also a limitation for widespread use of wave power on a string.

4. How does wave power on a string compare to other forms of renewable energy?

Wave power on a string has its own unique advantages and disadvantages compared to other forms of renewable energy. It is more consistent than solar or wind power, as waves are constantly generated by the ocean. However, it is less consistent compared to hydroelectric power, as the intensity of ocean waves can vary significantly. Additionally, the cost of installation and maintenance for wave power on a string can be higher compared to other renewable energy sources.

5. Is wave power on a string currently being used for energy production?

Yes, wave power on a string is being used in various locations around the world for energy production. Some countries, such as Scotland and Portugal, have implemented commercial-scale wave power projects, while others are still in the testing and development phase. However, due to the limitations and challenges mentioned earlier, it is not yet a widely used source of renewable energy.

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