A wave represented by the equation y1 = a cos (kx - ω t) is superimposed with another wave to form a stationary wave such that the point x = 0 is node. The equation for the other wave is

Question

A wave represented by the equation y1 = a cos (kx - ω t) is superimposed with another wave to form a stationary wave such that the point x = 0 is node. The equation for the other wave is (A) a cos(kx-ω t+π) (B) a cos(kx+ω t+π) (C) a cos(kx+ω t+(π/2)) (D) a cos(kx-ω t+(π/2))

Tardigrade Admin · Accepted Answer

Since the point x = 0 is a node and reflection is taking place from point x = 0. This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of

π

or a
path change of

\frac{λ}{2} .

So, if

y_{in c i d e n t} = a COS (k x - ω t)

\Rightarrow y_{in c i d e n t} = a COS (- k x - ω t + π)

= - a cos (ω t + k x)

Hence equation for the other wave

y = a cos (k x + ω t + π)

Q. A wave represented by the equation $y_{1}$ = $a cos (k x - ω t$ ) is superimposed with another wave to form a stationary wave such that the point $x = 0$ is node. The equation for the other wave is

$a cos (k x - ω t + π)$

$a cos (k x + ω t + π)$

$a cos (k x + ω t + \frac{π}{2})$

$a cos (k x - ω t + \frac{π}{2})$

Q. A wave represented by the equation y1​ = acos(kx−ωt) is superimposed with another wave to form a stationary wave such that the point x=0 is node. The equation for the other wave is

acos(kx−ωt+π)

acos(kx+ωt+π)

acos(kx+ωt+2π​)

acos(kx−ωt+2π​)

Q. A wave represented by the equation $y_{1}$ = $a cos (k x - ω t$ ) is superimposed with another wave to form a stationary wave such that the point $x = 0$ is node. The equation for the other wave is

$a cos (k x - ω t + π)$

$a cos (k x + ω t + π)$

$a cos (k x + ω t + \frac{π}{2})$

$a cos (k x - ω t + \frac{π}{2})$