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Two plane harmonic sound waves are expressed by the equations

y1 (x,t) = A cos (πx - 100 πt);

1 How many times does an observer hear maximum intensity in one second?

(A) 4 (B) 10 (C) 6 (D) 8

2 . What is the speed of the sound?

(A) 200 m/s (B) 180 m/s (C) 192 m/s (D) 96m/s

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

(A) 192 (B) 48 (C) 100 (D) 96

1 Answer

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Best answer

Correct option 1. (A)  2. (A)  200m/s  3.  (D)  96

Explanation:

 1.  In one second number of maximas is called the beat frequency.

2.  (A) Speed of wave v =  ω/K

3.  At x = 0, y = y1 + y2 = 2A cos 96πt cos 4 πt Frequency of cos (96 πt) function is 45 Hz and that of cos (4πt) function is 2Hz.

In one second, cos function becomes zero at 2f 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 1s. 

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