Waves Ques 14
14. Two waves are represented by the equations $y_1=a \sin (\omega t+kx+0.57) m$ and $y_2=a \cos (\omega t$ $+kx) m$, where $x$ is in meter and $t$ in sec. The phase difference between them is
[2011]
(a) $1.0$ radian
(b) $1.25$ radian
(c) $1.57$ radian
(d) $0.57$ radian
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Answer:
Correct Answer: 14.(a)
Solution:
- (a) Here, $y_1=a \sin (\omega t+k x+0.57)$
so, $\phi_1=0.57$
and $y_2=a \cos (\omega t+k x)$
$ =a \sin [\frac{\pi}{2}+(\omega t+k x)] $
so, $\phi_2=\pi / 2$
Phase difference, $\Delta \phi=\phi_2-\phi_1$
$=\frac{\pi}{2}-0.57=\frac{3.14}{2}-0.57=1.57-0.57 $
$=1 \text{ radian }$
BETA
