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The intensity level due to 2 waves of same frequency in a given medium is 1 bel and 4 bel. What is the ratio of their amplitudes?

I solved it in the following way:

L1 = 10 decibels

L2 = 40 decibels

Loudness(L) = 10(log(I/Io))

Where I= Intensity of sound, Io = Intensity of weakest audible sound

Therefore,

10 = 10[log(I1/Io)]

Similarly,

40 = 10[log(I2/Io)]

Solving we get,

I1 = 10 Watt/m^2

I2 = 10000 watt/m^2

Intensity is proportional to (amplitude)^2

I1/I2 = a1^2/a2^2

a1/a2 = [I1/I2]^(1/2)

i.e. a1/a2 = [1/1000]^(1/2)

= 1/[10^(3/2)]

Is it right?

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# Ratio of amplitudes of sound problem

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