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Old Jan 16th 2015, 03:21 AM   #1
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Help with basic question?

Two points on a string at x=0 and x=1 are observed as travelling harmonic wave passes. The transverse displacements of the two points are:

y1= 0.2sin(3PIt) and y2= 0.2 sin(3PIt+PI/8)

I have to deduce the wavelength and speed of the waves, and decide if the conclusions are unambiguous. However, I've only met questions where I deduce these values from using 'k', and I see no way of attaining 'k' in these formulae, so I'm stumped. Any ideas? Thank you!
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Old Jan 16th 2015, 06:27 AM   #2
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Not sure what you mean by 'k,' but I suggest you become familiar with the general for a wave function:

y(t) = A sin(wt+p)

where A = amplitude, w (omega) = angular velocity in radians/second and p (often written as the Greek letter phi) is the phase shift of the wave. In this case point 2 is phase shifted by and angle of pi/8 from point 1, so therefore it is 1/16 of cycle away from point 1. Hence one answer is that the wavelength is 16 times the distance between the two points; but it may also be 1/16 + k cycles, where k = 1, 2, 3, .... since sin(wt + pi/8) = sin(wti + k + 2 pi) = sin(wt+pi/8 + 4 pi) = ....

The speed of the wave comes from v = fL, where f = frequency in Hertz and L = wavelength. You can calculate frequency from f = w/(2 pi).

Last edited by ChipB; Jan 16th 2015 at 11:49 AM.
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