What Frequency Does a String Vibrate at in Its Second Harmonic?

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SUMMARY

The frequency of vibration for a string fixed at both ends and vibrating at its second harmonic can be calculated using the formula fn = n(v/2L). For a string length of 0.29 m and a wave speed of 115 m/s, the correct calculation yields a frequency of 198.3 Hz for the second harmonic (n=2). The confusion often arises from the interpretation of the variable 'n' in the equation, which represents the harmonic number.

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A string of length 0.29 m is fixed at both ends. The string is plucked and a standing wave is set up that is vibrating at its second harmonic. The traveling waves that make up the standing wave have a speed of 115 m/s. What is the frequency of vibration?



fn=n(v/2L)



I tried: 2f1=1(115m/s/2*0.29) then 2f1= 198.3 and I have both multiplied the answer by 2 and divided and both answers are wrong. The second harmonic is really throwing me for a loop. I am also confused about the n in the equation. Any help is greatly appreciated!
 
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If you are unsure about the formula, how about trying this approach: Try drawing what the second harmonic looks like, and then determine what the wavelength of the wave is in relation to the length of the string. See if you can work from there.
 

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