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Q.

A wave propagates on a string in positive x-direction with a speed of 40 cm/s. The shape of string at $t = 2 s$ is $y = 10 \cos \frac{x}{5}$ where x and y are in centimeter. The wave equation is

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a

$y = 10 \cos (\frac{x}{5} - 8 t)$

b

$y = 10 \sin (\frac{x}{5} - 8 t)$

c

$y = 10 \cos (\frac{x}{5} - 8 t + 16)$

d

$y = 10 \sin (\frac{x}{5} - 8 t + 16)$

answer is C.

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Detailed Solution

$\begin{array}{l} y = 10 \cos \frac{x}{5} at t = 2 sec take general equation \\ y = y = 10 \cos [(\frac{x - vt}{5}) + ϕ] at t = 2 \sec \\ \Rightarrow y = 10 \cos (\frac{x - 40 \times 2}{5} + ϕ) \\ = 10 \cos (\frac{x}{5} - 8 \times 2 + ϕ) y = 10, x = 0 \Rightarrow ϕ = 16 \\ \Rightarrow y = 10 \cos (\frac{x}{5} - 8 t + ϕ) \\ \Rightarrow y = 10 \cos (\frac{x}{5} - 8 t + 16) \end{array}$

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