wave_mechanics critical_thinking Question 1
Question: A wave disturbance in a medium is described by $ y(x,t)=0.02\cos ( 50\pi t+\frac{\pi }{2} )\cos (10\pi x) $ , where x and y are in metres and t in seconds
[IIT 1995]
Options:
A) A displacement node occurs at x = 0.15 m
B) An antinode occurs at x = 0.3 m
C) The wavelength of the wave is 0.2 m
D) The speed of the wave is 5.0 m/s
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=0.02\cos (10\pi x)\cos ( 50\pi t+\frac{\pi }{2} ) $ At node, amplitude = 0 $ \Rightarrow $ $ \cos (10\pi x)=0\Rightarrow 10\pi x=\frac{\pi }{2},\frac{3\pi }{2} $
$ \Rightarrow x=\frac{1}{20}=0.05 $ m, 0.15m ?..
At antinode, amplitude is maximum $ \Rightarrow $ $ \cos (10\pi x)=\pm 1\Rightarrow x=0,\pi ,2\pi ...
$
Therefore x = 0, 0.1m, 0.2m ? Now $ \lambda =2\times $ Distance between two nodes or antinodes = $ 2\times 0.1=0.2 $
$ m $ and $ \frac{2\pi vt}{\lambda }=50\pi t $
$ v=25\lambda =25\times 0.2 $
$ =5m/\sec $ .
BETA
