Question

If the ratio of intensities of two waves is 1 : 25, then the ratio of their amplitudes will be(a) 1 : 25(b) 5 : 1(c) 26 : 24(d) 1 : 5

Answer 1

let x be the common ratio betwewn the intensities
then I1 = 1 × x = x and I2 = 25 × x = 25x

Intensity is directly proportional to the square of the amplitude of the wave

So I1 = k ( a1 ) ^2 and I2 = k ( a2 ) ^2

Now I1 : I2 = I1 / I2 = k × ( a1 ) ^2 / k × ( a2 ) ^2
=> x / 25x = ( a1 ) ^2 / ( a2 ) ^2
=> 1 / 25 = ( a1 ) ^2 / ( a2 ) ^2
Taking square root on both sides we get
1 / 5 = a1 / a2
=> Required ratio = a1 : a2 = 1 : 5