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

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Waves & Sound

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

t = 0

sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave ?

Answer: (A)

Wave speed:

v = \frac{1.2}{0.3} = 4

cm/s. Wave number:

k = \frac{2 π}{λ} = \frac{2 π}{7.5} = \frac{4 π}{15} \approx 0.83

rad/cm. Angular frequency:

ω = v k = 4 \times 0.83 \approx 3.35

rad/s. Since the crest is at

x = 0

t = 0

, we use a cosine function with amplitude 2 cm:

y = 2 cos (k x - ω t) = 2 cos (0.83 x - 3.35 t)

cm.

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Single correct option