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The displacement due to a wave moving in the positive x-direction is given by y = 1/(1 +x2) at time t = 0 and by y = 1 / [1 + (x - 1)2] at t = 2 seconds, where x and y are in metres. The velocity of the wave in m/s is(a) 0.5 (b) 1 (c) 2 (d) 4 |
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Answer» Correct Answer is: (a) 0.5 We rewrite the given equation as y = 1/1 +(x - vt)2. For t = 0, this becomes y = 1 / (1 + x2), as given. For t = 2, this becomes y = 1 / [1 + (x - 2v)2] = 1 / [1 + (x - 1)2]. ∴ 2v = 1 or v = 0.5 m/s. |
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