# Problem on Loudness of Sound

1. Apr 29, 2007

### crossfacer

1. The problem statement, all variables and given/known data
The loudness of a sound heard at a point, a distance d = 10m from a small source of 125Hz, is 60phons. Provided that the intensity level of the sound heard at the point given is 70dB.

The threshold of pain is 120dB for all frequencies. How far from the source will a normal ear feel painful?

2. Relevant equations

For a small source, the intensity of sound, I is inversely proportional to d^2.
And intensity level = 10*log(I1 / I2)

3. The attempt at a solution
Let the required distance be x.

so, I1 / I2 = d2^2 / d1^2

70/120 = x^2 / 10^2

x = 7.64m

But the solution is:

Since intensity level difference = 120 -70 = 50dB

So, 50 = 10*log(10^2 / x^2)

x = 0.032m

What's wrong with my answer? Thank you so much!

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