wave_mechanics critical_thinking Question 20
Question: The equation of displacement of two waves are given as $ y _{1}=10\sin ( 3\pi t+\frac{\pi }{3} ) $ ; $ y _{2}=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t) $ . Then what is the ratio of their amplitudes
[AIIMS 1997; Haryana PMT 2000]
Options:
A) 1 : 2
B) 2 : 1
C) 1 : 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ y _{1}=10\sin ( 3\pi t+\frac{\pi }{3} ) $ …(i) and $ y _{2}=5[\sin 3\pi t+\sqrt{3}\cos 3\pi t] $
$ =5\times 2[ \frac{1}{2}\times \sin 3\pi t+\frac{\sqrt{3}}{2}\times \cos 3\pi t ] $
$ =10[ \cos \frac{\pi }{3}\sin 3\pi t+\sin \frac{\pi }{3}\cos \pi t ] $
$ =10[ \sin ( 3\pi t+\frac{\pi }{t} ) ] $ …
(ii) ($ \because $ sin(A + B) = sinA cosB + cosA sinB) Comparing equation (i) and (ii) we get ratio of amplitude 1 : 1.
BETA
