Wave Motion 5 Question 13
13. At $x=0$ how many times the amplitude of $y _1+y _2$ is zero in one second?
(2006, 5M)
(a) 192
(b) 48
(c) 100
(d) 96
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Answer:
Correct Answer: 13. (c)
Solution:
- At $x=0, y=y _1+y _2=2 A \cos 96 \pi t \cos 4 \pi t$
Frequency of $\cos (96 \pi t)$ function is $48 Hz$ and that of $\cos (4 \pi t)$ function is $2 Hz$.
In one second, cos function becomes zero at $2 f$ times, where $f$ is the frequency. Therefore, first function will become zero at 96 times and the second at 4 times. But second will not overlap with first. Hence, net $y$ will become zero 100 times in $1 s$.
