Calculating the fundamental frequency of a travelling wave

  • Thread starter savva
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  • #1
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No idea what to do here, really tough question, can i get some assistance please?

Homework Statement


The equation of a travelling transverse wave is
y=2.0sin 2π(x/30 - t/0.01)

where x and y are in centimetres and t is in seconds.

When attached at both ends, a string under a tension of 480 N and having a linear density of 1.20 x 10-2 kg/m resonates at a frequency of 150 Hz. The next highest frequency at which the string resonates is 200 Hz.

(i) What is the fundamental frequency of vibration for this string under this tension?

(ii) What is the string’s length?
 

Answers and Replies

  • #2
BruceW
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The equation of a travelling transverse wave is
y=2.0sin 2π(x/30 - t/0.01)

where x and y are in centimetres and t is in seconds.
What does this have to do with the rest of the question??

Also, for the question, are you supposed to derive the result from first principles, or just put in the values to the equation? Since you haven't written the equation for this situation, I'm guessing you're supposed to derive it from first principles... Have you been taught how to do that in class?
 
  • #3
sophiecentaur
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I could be picky and say that a travelling wave doesn't have a "fundamental frequency". A fundamental frequency implies a resonance which can only occur with a wave that is constrained to have multiple reflections (a standing or stationary wave). Of course, this can be considered as a wave travelling many times up and down the length of string / organ pipe / radio antenna but the modes are defined by the boundaries at each end as well as the wavelength.

The coefficients in the wave equation you are given will tell you the wavelength and the frequency. From that, you can calculate the speed and that is all you need to know about the wave. Look at the general equation for a travelling wave (all over the place for you to find) and the numbers 30 and 0.01 will give you the frequency and wavelength if you compare your equation with the one you find.

For the wave to resonate on the string, you need a whole number of half wavelengths. The fundamental will be when the string length is a half wavelength.
Try to take it from there rather than being given the whole answer in one go.
 

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