JEE Main 2025 Jan 23 Shift 2, Physics Q4: Types and Equations of Waves

JEE Main2025Jan 23, Shift 2Physics

The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 sin [20 \times 1 0^{- 3} x + 600 t]$ mm, where $x$ is in the mm and $t$ is in second. The velocity of the wave is :

A
$+ 30 m / s$
B
$- 60 m / s$
C
$- 30 m / s$
D
$+ 60 m / s$

Solution

Compare with the standard form $y = A sin (k x + ω t)$ . Here $ω = 600 s^{- 1}$ and $k = 20 \times 1 0^{- 3} m m^{- 1}$ .

Wave speed magnitude: $∣ v ∣ = \frac{ω}{k} = \frac{600}{20 \times 1 0 ^{- 3}} = 3 \times 1 0^{4} mm / s = 30 m / s .$

Because the argument is $k x + ω t$ (same sign), the wave moves in the $- x$ direction. So $v = - 30 m / s .$

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JEE Main 2025 Jan 23 Shift 2, Physics Q4: Types and Equations of Waves

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