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+1 vote
23.0k views
in Physics by (63.7k points)

Waves y1 = A xt cos(0.5πx - 100πt) and y2 = A xt cos(0.46πx - 92 πt) are travelling along x-axis. (Here x is in m and t is in second) 

1. The number of times intensity is maximum in time interval of 1 sec 

(a) 4 

(b) 6 

(c) 8 

(d) 10 

2. The wave velocity of louder sound is 

(a) 100 m/s 

(b) 192 m/s 

(c) 200 m/s 

(d) 96 m/s 

3. The number of times y1 + y2 = 0 at x = 0 in 1 sec is 

(a) 100 

(b) 46 

(c) 192 

(d) 96

1 Answer

+1 vote
by (71.1k points)
selected by
 
Best answer

Correct option: 1 - (a), 2 - (c), 3 - (d)

Explanation: 

The equations are y1 = A cos (0.5 πx – 100 πt) and y2 = A cos (0.46 πx – 92 πt) represents two progressive wave travelling in the same direction with slight difference in the frequency. This will give the phenomenon of beats. Comparing it with the equation y = A cos (kx – πt), we get

Note : Wave velocity is same because it depends on the medium in which the wave is travelling. 

Now, at x = 0

⇒ net amplitude is zero for n = 96 times 

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