JEE Main 2025 Apr 2 Shift 2, Physics Q6: Types and Equations of Waves

JEE Main2025Apr 2, Shift 2Physics

A sinusoidal wave of wavelength $7.5$ cm travels a distance of $1.2$ cm along the $x$ -direction in $0.3$ sec. The crest $P$ is at $x = 0$ at $t = 0$ sec and maximum displacement of the wave is $2$ cm. Which equation correctly represents this wave ?

A
$y = 2 cos (0.83 x - 3.35 t)$ cm
B
$y = 2 sin (0.83 x - 3.5 t)$ cm
C
$y = 2 cos (3.35 x - 0.83 t)$ cm
D
$y = 2 cos (0.13 x - 0.5 t)$ cm

Solution

Amplitude $A = 2$ cm (maximum displacement).

Wave speed $v = \frac{1.2 cm}{0.3 s} = 4$ cm/s.

Wave number $k = \frac{2 π}{λ} = \frac{2 π}{7.5} \approx 0.83$ cm $^{- 1}$ .

Angular frequency $ω = v k = 4 \times 0.83 \approx 3.35$ rad/s.

The condition that there is a crest at $x = 0$ when $t = 0$ rules out a sine function and forces a cosine. Travelling in $+ x$ direction gives the argument $(k x - ω t)$ .

$∴ y = 2 cos (0.83 x - 3.35 t)$ cm.

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JEE Main 2025 Apr 2 Shift 2, Physics Q6: Types and Equations of Waves

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