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Q.

The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 \sin [20 \times 10^{- 3} x + 600 t] mm$ , where x is in the mm and t is in second. The velocity of the wave is :

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a

– 60 m/s

b

+ 60 m/s

c

+ 30 m/s

d

– 30 m/s

answer is C.

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Detailed Solution

$y (x, t) = 4.0 \sin [20 \times 10^{- 3} x + 600 t] mm$
$\begin{array}{l} here, ω = 600 s^{- 1} \\ and, k = 20 \times 10^{- 3} {mm}^{- 1} \end{array}$
$∴ v = \frac{ω}{k} = \frac{600}{20 \times 10^{- 3}}$
$\begin{array}{l} = 30 \times 10^{- 3} mm / s \\ = 30 m / s \end{array}$
& direction is towards -ve x-axis
$∴$ v = – 30 m/s

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The equation of a transverse wave travelling along a string is y(x,t)=4.0sin⁡20×10−3x+600t mm, where x is in the mm and t is in second. The velocity of the wave is :