Calculating the power output from a persons mouth

[Aleisha]

Homework Statement

Speech at a distance of 45.1 cm has a sound level of 59.3 dB. Assuming that the energy in the sound spreads out equally in all directions from the person's mouth, calculate the total power output from the person.

Given:
Distance= 0.451m
Sound level 59.3 dB
P=? J

Homework Equations

I=P/A
A=4 x Pi x r^2

The Attempt at a Solution

A= 4 x Pi x 0.451^2
= 2.5560 m^2

I tried to find I (Intensity) by rearranging the; dB=10 log (I/Io) but isn't possible... So I'm a little stuck as to how to calculate the Intensity so I can substitute into the I=P/A equation. I know somehow I must use the given decibels at some point but I've been looking for an equation but can't find it.

Much appreciate if someone could help, thank you :)

 

[jbriggs444]

One reference that I googled up is https://en.wikipedia.org/wiki/Sound_power.

The relevant information is given in this passage:

For example, a sound at SPL = 85 dB or p = 0.356 Pa in air (ρ = 1.2 kg·m⁻³ and c = 343 m·s⁻¹) through a surface of area A = 1 m² normal to the direction of propagation (θ = 0 °) has a sound energy flux P = 0.3 mW

I would ignore the table at the top of that article. It does not have the appropriate units for your application -- it is reporting a distance-independent quantity.

 

[Aleisha]

Am i assuming that the particles are moving at a velocity of v=343m/s?

 

[jbriggs444]

Am i assuming that the particles are moving at a velocity of v=343m/s?

I do not see how particle velocity comes into it. If you have a power flux for 85db in milliwatts per square meter, that gives you enough information to compute a power flux for 59.3 db in milliwatts per square meter.