Calculate the Sound intensity level

[ninaw21]

Homework Statement

A jackhammer with a sound power of 10 W is operating in the countryside. Calculate the
intensity levels at distances of 2.0 m and 50.0 m from the jackhammer. Calculate the
corresponding levels in dB.

Homework Equations

β = (10dB) log (I/Io)
where, β = sound intensity level, I = intensity, Io= 1.0x10^-12 W/m^2

The Attempt at a Solution

I honestly have no idea how to do this question! Please help

 

[edgepflow]

Welcome to PF.

If you inspect your formula, you will notice that you need to find I. The definition of I is power per unit area: I = P / A.

Assume the jackjammer is a point source. Then A will be the surface area of a sphere. You are given the power.

Try this and show your work !

 

[berkeman]

Homework Statement

A jackhammer with a sound power of 10 W is operating in the countryside. Calculate the
intensity levels at distances of 2.0 m and 50.0 m from the jackhammer. Calculate the
corresponding levels in dB.

Homework Equations

β = (10dB) log (I/Io)
where, β = sound intensity level, I = intensity, Io= 1.0x10^-12 W/m^2

The Attempt at a Solution

I honestly have no idea how to do this question! Please help

Welcome to the PF.

It looks like the units of sound intensity are W/m^2:

http://en.wikipedia.org/wiki/Sound_intensity

So you would want to calculate the surface area that the 10W is going through at those distances away from the source, and use that surface area and the 10W number to figure out the sound intensity at those distances.

One question would be should you use a sphere's area or hemisphere's area for your surface that the sound is going through. I'm not sure which this problem assumes. I know which one I'd use based on the wording, but I don't know if it would be the same as the problem wants...


EDIT -- Edged out by edgepflow!

 

[ninaw21]

Thanks guys!