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

1. y = (0.02) sin (15.7x − 2010t)
2. y = (0.02) sin (15.7x + 2010t)
3. y = (0.02) sin (7.85x − 1005t)
4. y = (0.02) sin (7.85x + 1005t)

Correct answer: y = (0.02) sin (15.7x − 2010t)

Solution

The wavelength is calculated as λ = total length / number of waves = 4 m / 5 = 0.8 m. The wave number k = 2π/λ = 2π/0.8 = 7.85 rad/m. The angular frequency ω = 2πf, where f = v/λ = 128/0.8 = 160 Hz, so ω = 2π × 160 = 1005 rad/s. The wave equation is y = A sin(kx − ωt). Substituting A = 0.02 m, k = 7.85 rad/m, and ω = 1005 rad/s, the correct equation is y = (0.02) sin(7.85x − 1005t).

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