A solution to the 1D wave equation is B (x, t ) = A cos (kx - wt ) in reference

(a) Acos (k(x-u)-wt) which is equal to Acos(kx-wt-ku) (b)wave number = k angular frequency=w period= 2* pi /w

ID: 2127043 • Letter: A

Question

A solution to the 1D wave equation is B (x, t ) = A cos (kx - wt ) in reference frame O , where k > 0 is the

wave number and w is the angular frequency of the wave.

(a) How does this wave transform under a Galilean transformation to another inertial frame O' , moving

with velocity u(vector) = ux relative to O ? [2 points]

(b) What is the wave number, the angular frequency and the period of the wave in the new frame O0 in

terms of u ? Sketch B (0,t ) in both frames to show how the wave has changed shape. (The wave is not

invariant under the Galilean transformation. Assume uk < w. You may need to go back to your Physics

3 notes to nd the relationship between the angular frequency and the period. )

(a) Acos (k(x-u)-wt)

which is equal to Acos(kx-wt-ku)

(b)wave number = k

angular frequency=w

period= 2* pi /w

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