A wave in a string has an amplitude of 2cm. The wave travels in the positive direction of x- axis with a speed of 128 m/s and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is

Options

(a) y = (0.02) m sin (15.7x – 2010t)
(b) y = (0.02) m sin (15.7x + 2010t)
(c) y = (0.02) m sin (7.85x – 1005t)
(d) y = (0.02) m sin (7.85x + 1005t)

Correct Answer:

y = (0.02) m sin (7.85x – 1005t)

Explanation:

A = 2 cm, ? / k = 128 ms, 5λ = 4, λ = 4/5 m.
y = A sin ( kx – ?t),
k = 2π / λ = 2π x 5 / 4 = 31.4 / 4 = 7.85
y = 0.02m sin (7.857 – 1005 t)
? = 128 x 7.85 = 1005