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Question

Two waves whose equations of displacement of particles in the medium are y1=4sin(500πt25x) and y2=2sin(506πt30x). How many beats will generate due to the superposition of the two waves and what will be the relation between maximum (Imax) and minimum (Imin) intensity?
  1. 3 beats per second and Imax=2Imin
  2. 3 beats per second and Imax=9Imin
  3. 6 beats per second and Imax=9Imin
  4. 6 beats per second and Imax=2Imin


Solution

The correct option is B 3 beats per second and Imax=9Imin
Given:
y1=4sin(500πt25x)
y2=2sin(506πt30x)
Frequency of the first wave,
f1=ω12π=500π2π=250 Hz
and for the second wave,  
f2=ω22π=506π2π=253 Hz
Now, beat frequency,
fb=|f1f2|=3 Hz
3 beats per second. 
Now,
ImaxImin=(AmaxAmin)2
ImaxImin=(A1+A2A1A2)2=(4+242)2
ImaxImin=91
Imax=9Imin

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