Question

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. $y=a \sin (\omega t+k x)$
• B. $y=-a \sin (\omega t+k x)$
• C. $y=a \sin (\omega t-k x)$
• D. $y=-a \sin (\omega t-k x)$

Answer 1

Answer: (B)

Equation of a wave
$y=a \sin (\omega t-k x)$...(1)
Let equations of another wave may be,
$y=a \sin (\omega t +k x)$...(2)
$y=-a \sin (\omega t +k x)$...(3)
If Eq. (1) propagates with Eq. (2), then we get
$y=2 a \cos k x \sin \omega t$...(4)
If Eq. (1), propagates with Eq. (3), then we get
$y=-2 a \sin k x \cos \omega t$...(5)
After putting $x=0$ in Eqs.(4) and respectively, we get
$y=2 a \sin \omega t$ and $y=0$
Hence, Eq. (3) is a equation of unknown wave.