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

[shupert.11]

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!

 

[danago]

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.

 

[baba89]

The frequency of vibration in this scenario can be calculated using the formula fn = n(v/2L), where fn is the frequency, n is the harmonic number, v is the speed of the traveling wave, and L is the length of the string. In this case, we are looking for the frequency of the second harmonic, so n = 2. Plugging in the values given, we have:

fn = 2(115 m/s)/(2*0.29 m) = 400 Hz

This means that the string is vibrating at a frequency of 400 Hz. It is important to note that the harmonic number, n, represents the number of half wavelengths present in the standing wave. So for the second harmonic, there are two half wavelengths present in the standing wave. I hope this helps clarify any confusion you had.