Question

The equation of a wave disturbance is given as :

$y=0.02\sin (\frac{\pi }{2}+50\pi t)\cos \left(10\pi x\right)$, where $x$ and $y$ are in metres and $t$ is in seconds.

Choose the correct statement(s):

• A. the wavelength of wave is $0.2m$
• B. displacement node occurs at $x=0.15m$
• C. displacement antinode occurs at $x=0.3m$
• D. the speed of constituent waves is $0.2m/s$

Answer 1

Answer: (A), (B), (C)

The correct options are
A displacement node occurs at $x=0.15m$
B displacement antinode occurs at $x=0.3m$
C the wavelength of wave is $0.2m$

Wave length $=\frac{2\pi }{k}$ Here $k$ is $10\pi$
Thus wave length $=\frac{2}{10}=0.2$
At $x=0.15m$ we have cosine term becoming
zero. Thus there is a displacement node at $x=0.15m.$ At $x=0.3m$ we have cosine term being maximum negative i.e. $-1$. Thus there is a displacement antinode.