Question

Which of the following functions does not represent a stationary wave ? Here $a, b$ and care constants.

• A. $y=a \cos b x \sin c t$
• B. $y=a \sin b x \cos c t$
• C. $y=a \sin (b x +c t)$
• D. $y=a \sin (b x+ c t)+a \sin (b x -c t)$

Answer 1

Answer: (C)

$y=a \sin (b x +c t)$

Answer 2

Two superimposing waves are incident wave
$y_{1}=a \sin (\omega t-k x)$ and reflected wave
$y_{2}=a \sin (\omega t +k x)$
Then by principle of superposition
$y =y_{1}+y_{2}$
$=a[\sin (\omega t-k x)+\sin \omega t+ k x)]$
$\Rightarrow y=2 a \cos k x \sin \omega t$
Therefore, option (c) doesnot represent a stationary wave.