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Solution


Q.

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          [2025]
1 y = 2 cos (0.83x – 3.35t) cm  
2 y = 2 sin (0.83x – 3.5t) cm  
3 y = 2 cos (3.35x – 0.83t) cm  
4 y = 2 cos (0.13x – 0.5t) cm  

Ans.

(1)

v=distancetime

v=1.20.3=4 cm/s

k=2πλ=2π7.5=4π15=0.83

v=ωk ⇒ ω=vk=4×4π15=3.35

At t = 0, x = 0, there is a crest

So, y = A cos (kx – ωt)

∴  y = 2 cos (0.83x – 3.35t) cm