wave_mechanics critical_thinking Question 39
Question: The displacement due to a wave moving in the positive x-direction is given by $ y=\frac{1}{(1+x^{2})} $ at time $ t=0 $ and by $ y=\frac{1}{[1+{{(x-1)}^{2}}]} $ at $ t=2 $ seconds, where x and y are in metres. The velocity of the wave in m/s is
Options:
A) 0.5
B) 1
C) 2
D) 4
Show Answer
Answer:
Correct Answer: A
Solution:
In a wave equation, x and t must be related in the form $ (x-vt) $ .
We rewrite the given equations $ y=\frac{1}{1+{{(x-vt)}^{2}}} $ For $ t=0, $ this becomes $ y=\frac{1}{(1+x^{2})} $ , as given For $ t=2, $ this becomes $ y=\frac{1}{[1+{{(x-2v)}^{2}}]}=\frac{1}{[1+{{(x-1)}^{2}}]} $
Therefore $ 2v=1 $ or $ v=0.5m/s $ .
BETA
