Displacement of a wave is expressed as . The wavelength of the wave when its velocity is 300 m/s is [2025]

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Solution

Q.
Displacement of a wave is expressed as $x (t) = 5 \cos (628 t + \frac{π}{2}) m$ . The wavelength of the wave when its velocity is 300 m/s is [2025]

1 5 m

2 3 m

3 0.5 m

4 0.33 m

Ans.
(2)

$x (t) = 5 \cos [628 t + \frac{π}{2}] m$

Wave velocity v = 300 m/s

$v = \frac{ω}{k}$

$300 = \frac{628}{K} \Rightarrow K = \frac{628}{300} m^{- 1}$

$\frac{2 π}{λ} = \frac{628}{300} \Rightarrow λ = \frac{2 \times 3.14 \times 300}{628}$

$\Rightarrow λ = 3 m$

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