Q162 / 225 · JEE Main 2002 · Physics

A wave $y=a \sin (\omega t-k x)$ on a string meets with another wave producing a node at $x=0$. Then the equation of the unknown wave is

  • A
    $y=a \sin (\omega t+k x)$
  • Correct answer
    B
    $y=-a \sin (\omega t+k x)$
  • C
    $\mathrm{y}=\mathrm{a} \sin (\omega \mathrm{t}-\mathrm{kx})$
  • D
    $\mathrm{y}=-\mathrm{a} \sin (\omega \mathrm{t}-\mathrm{kx})$

Solution

$y_1+y_2=a \sin (\omega t-k x)-a \sin (\omega t+k x)$ $=-2 a \cos \omega t \times \sin k x \Rightarrow y_1+y_2=0$ at $x=0$

Hence, the correct answer is option: 'B'.

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