A fan at a rock concert is 45.0 m from the stage, and at this point the sound intensity level is 108 dB. Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate . Typically, the diameter of this membrane is about 8.40 m in humans
I solved for the intensity using Beta = (10 dB) log I/I_0
I got I to be 3.11*10^-5 W/m^2 45m away.
Then I found the energy to be 17.22*10^-11J
The answer wants it in micro joules but I'm not even sure if I've done the problem correctly.
I don't understand the diamter being 8meters. It makes no sense.
Secondly, What is the exact question?
oh sorry the diameter is 8.4mm
and the question is asking for the
How much energy is transferred to her eardrums each second ?
108=10 log(I/Io)
10.8=log( )
I= 10^10.8 * Io=10^10.8*1E-12=.063watts/m^2 check that.
Energy= areadrum*I= PI* .004^2*I above.
= .063watts/m^2*PI*16E-6=3.2 × 10-6 watts.
108=10 log(I/Io)
10.8=log( )
I= 10^10.8 * Io=10^10.8*1E-12=.063watts/m^2 check that.
power= areadrum*I= PI* .004^2*I above.
= .063watts/m^2*PI*16E-6=3.2 × 10-6 joules/sec
energy in one second= 3.2E-6joules
The range away from the stage doesn't matter?
the range doesnt matter because the relative intesity is already given in db
To solve the problem correctly and find the answer in microjoules, you'll need to follow these steps:
1. Convert the sound intensity level from decibels (dB) to watt per square meter (W/m^2) using the formula:
I = I_0 * 10^(Beta/10)
where I is the sound intensity, I_0 is the reference intensity (typically 10^(-12) W/m^2), and Beta is the sound intensity level in dB.
In this case, Beta = 108 dB. Substituting these values into the formula:
I = (10^(-12) W/m^2) * 10^(108/10)
≈ 3.16 * 10^(-3) W/m^2
2. Calculate the energy using the formula:
Energy = Sound Intensity * Area
The area of the tympanic membrane is given as 8.40 m^2.
Energy = (3.16 * 10^(-3) W/m^2) * 8.40 m^2
≈ 2.66 * 10^(-2) W
3. Convert the energy from watts to microjoules (µJ). There are 10^6 µJ in a joule.
Energy = 2.66 * 10^(-2) W * 10^6 µJ/W
≈ 2.66 * 10^4 µJ
Please note that the value you obtained, 17.22 * 10^(-11) J, seems incorrect. Double-check your calculations to make sure you applied the formulas correctly.