A wave is represented by the equation $y = A sin (10 π x + 15 π t + π / 3)$ , where $x$ is in metres and $t$ is in seconds. What is the wavelength of this wave travelling in the positive x-direction?

0.5 m

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0.2 m

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0.25 m

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0.75 m

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Solution

The correct option is D $0.2 m$
The equation of the wave is $y = A sin (10 π x + 15 π t + π / 3)$
This can be written in the standard form as
$y = A sin 2 π (\frac{t}{T} - \frac{x}{λ} + ϕ)$ , where $T$ is period and $λ$ is phase difference.
$y = A sin 2 π (\frac{15 π t}{2 π} + \frac{10 π x}{2 π} + \frac{π}{6 π})$
$= A sin 2 π (\frac{t}{\frac{2}{15}} + \frac{x}{\frac{1}{5}} + \frac{1}{6})$
Comparing this with standard equation
$λ = \frac{1}{5}$ and $T = \frac{2}{15}$
$∴$ wavelength $λ = 0.2 m$

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