Standing question - real straightforward- Workings given

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elemis
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Printed exam question (iii) giving the standing wave y(x,t) = 0.1 sin(15.71x) cos(27.2t) in SI units, asking for the angular frequency, wavevector, amplitude and velocity of the two travelling waves, and the harmonic for a 0.8 m string.


W= 27.2

K=15.71

A=0.1

Now to determine the harmonic.

Formula for wavenumber k_n equals (2n minus 1) times pi divided by 2L, with n as the mode index and L as the string length.


This formula gives the harmonic to be 4.5. This can't be possible since n has to be an integer.

I realize this wave has a node at one end and an anti node at the other.

I also realize that this wave on the string has a wavelength =0.4 by using K=2pi/lambdaWhat do I do ? :(
 

Discussion

Or am I wrong in assuming this is a wave has a node at one end and an anti node at the other ?