SATHEE: Wave Motion 1 Question 1

Wave Motion 1 Question 1

1. A progressive wave travelling along the positive $x$ -direction is represented by $y (x, t) = A \sin (k x - ω t + ϕ)$ . Its snapshot at $t = 0$ is given in the figure.

(2019 Main, 12 April I)

For this wave, the phase $ϕ$ is

(a) $- \frac{π}{2}$

(b) $π$

(d) $\frac{π}{2}$

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Answer:

Correct Answer: 1. (b)

Solution:

From the given snapshot at $t = 0$ ,

$y = 0 at x = 0$

and $y = - ve$ when $x$ increases from zero.

Standard expression of any progressive wave is given by $y = A \sin (k x - ω t + ϕ)$

Here, $ϕ$ is the phase difference, we need to get

at $t = 0 y = A \sin (k x + ϕ)$

Clearly $ϕ = π$ , so that

$\begin{aligned} y = A \sin (k x + π) \\ \Rightarrow & y = - A \sin (k x) \\ and & y & = 0 at x = 0 \\ y & = - ve at x > 0 \end{aligned}$

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Wave Motion 1 Question 1

1. A progressive wave travelling along the positive x-direction is represented by y(x,t)=Asin⁡(kx−ωt+ϕ). Its snapshot at t=0 is given in the figure.

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1. A progressive wave travelling along the positive $x$ -direction is represented by $y (x, t) = A \sin (k x - ω t + ϕ)$ . Its snapshot at $t = 0$ is given in the figure.