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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
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The correct answer is:
$y=-a \sin (\omega t+k x)$
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
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
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