wave_mechanics interference_and_superposition_of_waves Question 17
Question: Two waves $ y _{1}=A _{1}\sin (\omega t-{\beta _{1}}) $ , $ y _{2}=A _{2}\sin (\omega t-{\beta _{2}}) $ Superimpose to form a resultant wave whose amplitude is
[CPMT 1999]
Options:
A) $ \sqrt{A _{1}^{2}+A _{2}^{2}+2A _{1}A _{2}\cos ({\beta _{1}}-{\beta _{2}})} $
B) $ \sqrt{A _{1}^{2}+A _{2}^{2}+2A _{1}A _{2}\sin ({\beta _{1}}-{\beta _{2}})} $
C) $ A _{1}+A _{2} $
D) $ |A _{1}+A _{2}| $
Show Answer
Answer:
Correct Answer: A
Solution:
Phase difference between the two waves is $ \varphi =(\omega t-{\beta _{2}})=(\omega t-{\beta _{1}})=({\beta _{1}}-{\beta _{2}}) $ \Resultant amplitude $ A=\sqrt{A _{1}^{2}+A _{2}^{2}+2A _{1}A _{2}\cos ({\beta _{1}}-{\beta _{2}})} $
BETA
