pain from sound?
At a distance of 13 km, a 140 Hz horn, assumed to be a point source, is barely audible. At what distance would it begin to cause pain? (Pain Threshold = 120dB)
At a distance of 13 km, a 140 Hz horn, assumed to be a point source, is barely audible. At what distance would it begin to cause pain? (Pain Threshold = 120dB)
benaddict
Favorite Answer
0.04111 km.
Using Intensity (in dB) = 10 log_10(I/I_0), where I_0 = 10^(-12)
Barely perceptible sound = 0 dB, hence I = 10^(-12) Watt
Now power of the point source is P= I(4 pi R^2) where R = 13000 meters.
Now Intensity at R2 distance is 120 dB, so I2 = 1 Watt
Equating power of the source as constant in both locations
I(4 pi R^2) = I2 (4 pi R2^2)
giving a value of 0.04111 km for R2.