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The equation of a wave traveling on a string is given by $y = 8 \sin [(5 m^{- 1}) x - (4 s^{- 1}) t]$ . Then

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The displacement of a particle of the string at $t = 0$ and $x = \frac{π}{30} m$ from the mean position is $4 m$

The displacement of a particle from the mean position at $t = 0, x = \frac{π}{30} m$ is $8 m$

Both A & B

Velocity of wave is $0.8 \frac{m}{s}$

answer is D.

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Detailed Solution

Given $y = 8 \sin [(5 m^{- 1}) x - (4 s^{- 1}) t]$ …(1)

Wave equation $y = A \sin (k t - ω x) ... (2)$

Compare (1) & (2)

$ω = 4 s^{- 1}$ $k = 5 s^{- 1}$

We know $ϑ = \frac{ω}{k} = \frac{4}{5} = 0.8$

Position at $t = 0$ $x = \frac{π}{30} m$

$y = 8 \sin [5 (\frac{π}{30}) - 4 (0)]$

$y = 8 \sin \frac{π}{6}$

$y = 8 \times \frac{1}{2}$

$y = 4 m$

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