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A wave is represented by the equation : $y = A \sin (10 π x + 15 π t + π / 3)$ where x is in metre and t is in second. The expression represents.

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a wave travelling in the positive x-direction with a velocity 1.5 m/s

a wave travelling in the negative x-direction with a velocity 1.5 m/s

a wave travelling in the negative x-direction with a wavelength 0.2 m

a wave travelling in the positive x-direction with a wavelength 0.2 m

answer is B, C.

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Detailed Solution

$ω = 15 π, k = 10 π$
Speed of wave $v = \frac{ω}{k} = 1.5 m / s$
Wavelength of wave $λ = \frac{2 π}{k} = \frac{2 π}{10 π} = 0.2 m$
$10 π x and 15 π t$ have the same sign.
Therefore, wave is travelling in negative x-direction.

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