Q. Equation of a progressive wave is given by $y= sinbegin {pmatrix}frac{t}{2}-frac{x}{2}end{pmatrix}$, where $t$ is in seconds and $x$ is in metre. Then the distance through which the wave moves in $8$ second is (in metre).

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Equation of a progressive wave is given by $y= sinbegin {pmatrix}frac{t}{2}-frac{x}{2}end{pmatrix}$, where $t$ is in seconds and $x$ is in metre. Then the distance through which the wave moves in $8$ second is (in metre).

Solution:

Standard equation of a progressive wave is;

$ y = a, sin , 2pi left(frac{t}{T} – frac{x}{lambda} right)$

The given equation $y = a , sin , pi left( frac{t}{2} – frac{x}{4} right) $ can be written as

$y = a , sin , 2 pi left( frac{t}{4} -frac{x}{8} right)$

Comparing eqn. (i) and (ii), T = 4s and $lambda$ = 8m

Distance = Velocity $times $ Time = $frac{lambda}{T} times t = frac{8}{4} times 8 $ = 16 m