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Question

Two waves of equal frequencies have their amplitudes in the ratio of 3:5. They are superimposed on each other. The ratio of maximum and minimum intensities of the resultant wave is

A
16:1
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B
1:16
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C
8:1
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D
1:8
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Solution

The correct option is A 16:1
Given,
A1A2=35

As we know, IA2

I1I2=35 .......(1)

The formula for the resultant intensity is given by,

I=I1+I2+2I1I2cosϕ

Maximum intensity is obtained, when
cosϕ=1

Imax=(I1+I2)2

Minimum intensity is obtained, when
cosϕ=1

Imin=(I1I2)2

Hence,
ImaxImin=(I1+I2I1I2)2=⎜ ⎜ ⎜ ⎜ ⎜ ⎜I1I2+1I1I21⎟ ⎟ ⎟ ⎟ ⎟ ⎟2

Putting the value fron equation (1),

ImaxImin==⎜ ⎜ ⎜35+1351⎟ ⎟ ⎟2=161=16:1
​​​​​​​
Hence, option (A) is correct.

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