Waves

JEE Main level, single correct, medium

28 of 142

Question 28 of 142

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

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Answer: (B) −30 m/s-30 \mathrm{~m} / \mathrm{s}

$\begin{aligned}
& k=20 \times 10^{-3} \mathrm{~mm}^{-1}=20 \mathrm{~m}^{-1} \\
& w=600 \mathrm{~s}^{-1} \\
& v=\frac{W}{k}=\frac{600}{20}=30 \mathrm{~m} / \mathrm{s}
\end{aligned}$
and x&tx \& t carry same sign
Therefore v=−30 m/s\mathrm{v}=-30 \mathrm{~m} / \mathrm{s}

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