Waves · Question 18

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?

1. y = 2 (0.83x - 3.35t) cm
2. y = 2 (0.83x - 3.5t) cm
3. y = 2 (0.13x - 0.5t) cm
4. y = 2 (3.35x - 0.83t) cm

Answer

(1) y = 2 (0.83x - 3.35t) cm

Solution

Amplitude A = 2 cm

Wave speed v = 1.20.3 = 4 cm s-1

Wave number k = 2 = 2 7.5 0.83 cm-1

Angular frequency = kv = 0.838 4 3.35 rad s-1

Crest (maximum y) at x = 0, t = 0 cosine form with zero phase: y = A (kx - t)

Wave moves along +x (kx - t)

y = 2 (0.83x - 3.35t) cm

Answer: (1)