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JEE Main 202523 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
23 January
Shift
Evening Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2025 · 23 January · Evening Shift · Physics · Waves and Sound

The equation of a transverse wave travelling along a string is y(x,...

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 :

Options

  1. A−60 m/s-60 \mathrm{~m} / \mathrm{s}
  2. B−30 m/s-30 \mathrm{~m} / \mathrm{s}
  3. C+30 m/s+30 \mathrm{~m} / \mathrm{s}
  4. D+60 m/s+60 \mathrm{~m} / \mathrm{s}

Correct answer

B. −30 m/s-30 \mathrm{~m} / \mathrm{s}

Step-by-step solution

k=20×10−3 mm−1=20 m−1w=600 s−1v=Wk=60020=30 m/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 \& t carry same sign Therefore v=−30 m/s\mathrm{v}=-30 \mathrm{~m} / \mathrm{s}
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