posted by Edwin on .
A plane progressive wave is represented by the equation: y= 0.1sin(200pi(t)-20pi(x/17) where y is the displacement in millimetres, t is in seconds and x is the distance from a fixed origin O in metres. Find (i) the frequency of the wave, (ii) its wavelength (iii) its speed, (iv) the phase difference in radians between a point 0.25m from O and a point 1.10m from O.
(i) For the frequency f, require that
200*pi*t = 2*pi*f*t
and solve for f. Obviously f = 100 Hz
(ii) For the wavelength L, require that
20 pi (x/17) = 2 pi (x/L).
That means in this case
10/17 = 1/L
L = 1.7 meters.
(iii) The wave speed is f*L = 170 m/s
(iv) The phase difference can differ by added multiples of 2 pi. I assume you want the minimum phase difference.
The difference between 1.1 and 0.25 is 0.85 m. That is 1/2 of a wavelength, so that would be the phase shift.