Adjoining figure shows the snapshot of two waves A and B at any time t- The equation for A is y - A sin kx - - t - - and for B it is y - A sin kx - - t- It is clearly shown in the figure that wave A is ahead of B by a distance -k-The motion of a single point in time- i-e- y versus t for two waves is best represented by

The equation for wave A can be rewritten as y = A sin [kx ω t ϕ] = A sin [k(x ϕ/k ω t)] A sin [ k ω ( t + ϕ/k ) ] While equation of wave B is y = A s ...

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Byju's Answer

Standard XI

Physics

y-x-t Graph

Adjoining fig...

Question

Adjoining figure shows the snapshot of two waves A and B at any time t. The equation for A is $y = A s i n (k x - ω t - ϕ)$ , and for B it is y = A sin $(k x - ω t)$ . It is clearly shown in the figure that wave A is ahead of B by a distance $\frac{ϕ}{k}$ .

The motion of a single point in time, i.e., y versus t for two waves is best represented by

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Solution

The correct option is B
The equation for wave A can be rewritten as
$y = A s i n [k x - ω t - ϕ]$
$= A s i n [k (x - \frac{ϕ}{k} - ω t)]$
$A s i n [k - ω (t + \frac{ϕ}{k})]$
While equation of wave B is $y = A s i n (k x - ω t)$ .
Comparing above equations, we can easily conclude that A is at a distance ahead of $\frac{ϕ}{k}$ from B or wave
A is ahead of B by a time difference of $\frac{ϕ}{ω}$ . So, (b) is the correct option.

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