Pain Threshold - Reducing Intensity

[05holtel]

Homework Statement

At a distance of 30 m the noise from the engine of an jet has an intensity of 130 dB.

At this level, you will be in pain and your ears will hurt. That's why this intensity is know as the "pain threshold".

How far do you have to be from a jet (total distance), in order for the noise to drop down in intensity to 62.2 dB, a level comparable to that of a spoken conversation?

Express the result in the unit m, and to three significant figures.

Homework Equations

I think Intensity is proportional to (1/r^2)

I = (dE/dt) / 4pi(r^2)

I=1/2v(w^2)(A^2) where w = the angular frequency and A - the amplitude

The Attempt at a Solution

I am not sure how to manipulate the equations

 

[05holtel]

PLease help


I was trying the formula I2/I1 = A1/A2 = 4pi(r1^2)/ 4pi(r2^2)

I got 30.4 which is wrong

 

[kerimek]

to solve for the distance. However, I can provide some information on the pain threshold and how it relates to intensity.

The pain threshold, also known as the pain tolerance level, is the point at which a stimulus is perceived as painful. In the case of sound, this threshold is typically around 120 dB for most individuals. This means that at an intensity of 120 dB, the sound is perceived as painful.

In order to reduce the intensity of the sound from 130 dB to 62.2 dB, we can use the inverse square law, which states that the intensity of a sound is inversely proportional to the square of the distance from the source. This means that if we double the distance from the source, the intensity will decrease by a factor of 4.

Using this information, we can set up the following equation:

130 dB / 62.2 dB = (30 m / x m)^2

Solving for x, we get x = 60.1 m. This means that in order for the intensity of the sound from the jet to drop from 130 dB to 62.2 dB, you would need to be 60.1 m away from the jet.

It is also important to note that the pain threshold can vary from person to person and can also be affected by factors such as age, exposure to loud noises, and individual sensitivity. Therefore, the exact distance may vary for different individuals.