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Q.

In the superposition of two coherent waves (at x=0) given by y1=4sin300πt and y2=2sin308πt

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a

The frequency of the resulting wave is 152 Hz.

b

The amplitude of resulting wave varies at a frequency of 2 Hz.

c

The frequency of beats is 8 Hz.

d

The ratio of maximum to minimum intensity is 9.

answer is A, B, D.

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Detailed Solution

y=y1+y2=4sin300πt+2sin308πt.

 If we ignore unequal amplitudes

y=sin300πt+sin308πt

 =2sin300πt+308πt2cos300πt308πt2

 =2cos4πtsin304πt

 =Acos4πtsin304πt.

Frequency of amplitude variation =4π2π=2Hz.

Resultant frequency ω2π=304π2π=152Hz.

Number of beats = n2n1=4Hz

lmaxlmin=(a1+a2)2(a1a2)2=(4+2)2(42)2=364=91

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