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!

 

[asteriatic]

!

Hi there,

As a scientist, it's important to have a solid understanding of sound intensity levels and how to calculate them. Let's break down this problem step by step.

First, we need to understand that sound intensity is a measure of the amount of sound energy passing through a unit area per unit time. It is measured in watts per square meter (W/m^2).

In this problem, we are given the sound power of the jackhammer, which is 10 W. This means that 10 watts of sound energy is being produced by the jackhammer every second.

To calculate the sound intensity at a distance of 2.0 m, we can use the inverse square law, which states that the intensity is inversely proportional to the square of the distance. So, at a distance of 2.0 m, the sound intensity would be 10 W / (2.0 m)^2 = 2.5 W/m^2.

To calculate the sound intensity at a distance of 50.0 m, we would use the same formula, but with a distance of 50.0 m. This would give us an intensity of 10 W / (50.0 m)^2 = 0.04 W/m^2.

Now, to calculate the sound intensity level (β), we can use the formula given in the problem: β = (10 dB) log (I/Io). Plugging in the values for I and Io from our calculations above, we get:

- At 2.0 m: β = (10 dB) log (2.5 W/m^2 / 1.0x10^-12 W/m^2) = 123 dB
- At 50.0 m: β = (10 dB) log (0.04 W/m^2 / 1.0x10^-12 W/m^2) = 107 dB

These are the sound intensity levels at the given distances. To put them in context, a normal conversation is around 60 dB, so the jackhammer would be significantly louder at both distances.

I hope this helps you understand how to calculate sound intensity levels. Don't hesitate to ask for clarification if you need it. Good luck with your studies!