SATHEE: Wave Motion 5 Question 13

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

(d) 96

Objective Questions II (One or more correct option)

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Solution:

At $x = 0, y = y_{1} + y_{2} = 2 A \cos 96 π t \cos 4 π t$

Frequency of $\cos (96 π t)$ function is $48 H z$ and that of $\cos (4 π t)$ function is $2 H z$ .

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 $1 s$ .

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Wave Motion 5 Question 13

13. At x=0 how many times the amplitude of y1+y2 is zero in one second?

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13. At $x = 0$ how many times the amplitude of $y_{1} + y_{2}$ is zero in one second?