wave_mechanics interference_and_superposition_of_waves Question 26
Question: Two waves having equations $ x _{1}=a\sin (\omega t+{\varphi _{1}}) $ , $ x _{2}=a\sin (\omega t+{\varphi _{2}}) $ If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is
[CBSE PMT 2001]
Options:
A) $ \frac{\pi }{6} $
B) $ \frac{2\pi }{3} $
C) $ \frac{\pi }{4} $
D) $ \frac{\pi }{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
Superposition of waves does not alter the frequency of resultant wave and resultant amplitude
Therefore $ a^{2}=a^{2}+a^{2}+2a^{2}\cos \varphi =2a^{2}(1+\cos \varphi ) $
Therefore $ \cos \varphi =-1/2=\cos 2\pi /3 $ $ \varphi =2\pi /3 $
BETA
