wave_mechanics progressive_waves Question 2
Question: Equation of a progressive wave is given by $ y=0.2\cos \pi ( 0.04t+.02x-\frac{\pi }{6} ) $ The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of $ \pi /2 $
Options:
A) 4 cm
B) 8 cm
C) 25 cm
D) 12.5 cm
Show Answer
Answer:
Correct Answer: C
Solution:
Comparing with $ y=a\cos (\omega t+kx-\varphi ) $ , We get $ k=\frac{2\pi }{\lambda }=0.02\Rightarrow \lambda =100cm $ Also, it is given that phase difference between particles $ \Delta \varphi =\frac{\pi }{2}.
$
$ $ Hence path difference between them $ \Delta =\frac{\lambda }{2\pi }\times \Delta \varphi =\frac{\lambda }{2\pi }\times \frac{\pi }{2}=\frac{\lambda }{4}=\frac{100}{4}=25cm $
BETA
