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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 $128 m / s$ 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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$y = (0.02) m \sin (15.7 x - 2010 t)$

$y = (0.02) m \sin (7.85 x - 1005 t)$

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

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

answer is A.

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Detailed Solution

$A = 2 cm = 0.02 m λ = \frac{4}{5} = 0.8 m and f = \frac{v}{λ} = \frac{128}{0.8} = 160 Hz equation will be y = Asin (\frac{2 π}{λ} x - 2 πft) = 0.02 \sin (\frac{2 π}{0.8} x - 320 πt) = 0.02 \sin (7.85 x - 1005 t)$

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