Q107 / 125 · BITSAT 2010 · Physics
A wave $y=a \sin (\omega t-k x)$ on a string meets with another wave producing a node at $\mathrm{x}=0 .$ Then the equation of the unknown wave is
- A$y=a \sin (\omega t+k x)$
- Correct answerB$y=-a \sin (\omega t+k x)$
- C$y=a \sin (\omega t-k x)$
- D$y=-a \sin (\omega t-k x)$
Solution
Equation of a wave $y_{1}=a \sin (\omega t-k x)$....(i)
Let equations of another wave may be, $y_{2}=a \sin (\omega t+k x)$....(ii)
$y_{3}=-a \sin (\omega t+k x) \quad \ldots .$ (iii)
If Eq. (i) propagate with Eq. (ii), we get $\mathrm{y}=2 \mathrm{a} \cos \mathrm{kx} \sin \omega \mathrm{t}$
If Eq. (i), propagate with Eq. (iii), we get $y=-2 a \sin k x \cos \omega t$
At $x=0, y=0,$ wave produce node
So, Eq.(iii) is the equation of unknown wave
Hence, the correct answer is option: 'B'.