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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 ms^-1 and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is

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y = (0.02) sin(7.85x + 1005t ) m

y = (0.02) sin(15.7x + 2010t ) m

y = (0.02)sin(15.7x – 2010t ) m

y = (0.02) sin(7.85x – 1005t ) m

answer is D.

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Detailed Solution

y = A sin(kx - $ω$ t) ; A = 2cm = 0.02m
$λ = \frac{4}{5} = 0.8 m; k = \frac{2 π}{λ} = \frac{2 x 3.14}{0.8} = 7.85 n = \frac{v}{λ} = \frac{128}{0.8} = 160; ω = 2 πn = 2 π x 160 = 1005$

So the wave equation will be y = (0.02)m sin(7.85x–1005t)

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