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 mm and t is in second. The velocity of the wave is: (a) -60 m/s (b) +60 m/s (c) +30 m/s (d) -30 m/s

Answer: (d). k = 20 × 10⁻³ mm⁻¹, ω = 600 s⁻¹ v = (ω)/(k) = (600)/(0.02) = 3 × 10⁴ mm/s = 30 m/s kx and ω t have the same sign, so the wave moves along -x. So the answer is (d) -30 m/s.

The equation of a transverse wave travelling along a string is y(x… | JEE Main 2025 (23 Jan, Shift 2)

Q27JEE Main 2025 · 23 JAN · SHIFT 2Easy

Progressive Wave Equation

The equation of a transverse wave travelling along a string is

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

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Answer: (d)

$k = 20 \times 10^{-3}\text{ mm}^{-1}$ , $\omega = 600\text{ s}^{-1}$
$v = \dfrac{\omega}{k} = \dfrac{600}{0.02} = 3 \times 10^{4}\text{ mm/s} = 30\text{ m/s}$
$kx$ and $\omega t$ have the same sign, so the wave moves along $-x$ .
So the answer is (d) $-30\text{ m/s}$ .

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Progressive Wave Equation question from JEE Main 2025 (23 Jan, Shift 2)

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