The shape of a wave propagating in the positive x or negative x- direction is given y = $\frac{1}{\sqrt{1+x^2}}$ at t = 0 and y = $\frac{1}{\sqrt{2-2x+x^2}}$ at t = 1s where x and y are in meters. The shape the wave disturbance does not change during propagation. Find the velocity of the wave.
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Question

The shape of a wave propagating in the positive x or negative x- direction is given y = 1 1 + x 2 \frac{1}{\sqrt{1+x^2}} 1 + x 2 1 at t = 0 and y = 1 2 − 2 x + x 2 \frac{1}{\sqrt{2-2x+x^2}} 2 − 2 x + x 2 1 at t = 1s where x and y are in meters. The shape the wave disturbance does not change during propagation. Find the velocity of the wave.

Physics · Wave Motion

G1 Physics · Accepted Answer

Step 1: At t=0 the shape is F(x)=1/√(1+x²). At t=1, the shape is 1/√[(x-1)²+1]=F(x-1). Step 2: The entire profile has shifted by +1 m in 1 s. Hence speed = 1 m s⁻¹ in +x. Final: A.