Wave motionMediumBloom L3
Question
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 of the wave disturbance does not change during propagation, then the velocity of the wave is
Options
A.1 m/s in positive x direction
B.1 m/s in negative x direction
C.$\frac{1}{2}$ m/s in positive x direction
D.$\frac{1}{2}$ m/s in negative x direction
Solution
Sol. $y = \frac{1}{\sqrt{1 + x^{2}}}$ $att = 0$
$y = \frac{1}{\sqrt{x^{2}–2x + 2}}$ $att = 1$
= $\frac{1}{\sqrt{(x - 1)^{2} + 1}}$
$\because y = \frac{1}{\sqrt{1 + (x - t)^{2}}}$
v = 1 m/s towards the x-axis.
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