Question

Two waves
$y_1=Asin(\omega t-kx)and{y}_2=Asin(\omega t+kx)$
superimpose to produce a stationary wave then,

• A. $x=0$ is a node
• B. $x=0$ is an antinode
• C. $x=\frac{\pi }{k}$ is a node
• D. $x=\frac{2\pi }{k}$ is an antinode

Answer 1

Answer: (B), (D)

The correct options are
B $x=0$ is an antinode
D $x=\frac{2\pi }{k}$ is an antinode

Adding $y_1$ and $y_2$
we get:
$y=2Asin\omega tcoskx$
The nodes are when $coskx=0$
or $x=\frac{\pi }{2k}$ or $x=\frac{3\pi }{2k}$
The antinodes are when $coskx=-+1$ (plus or minus one)
or $x=0$ and $x=\frac{\pi }{k}$ and $x=\frac{2\pi }{k}$
Hence option B and D are true.