At a concert, the loudness of sound, L, in decibels, is given by the equation L=10log(I/I_o), where I is the intensity, in watts per square metre, and I_o, is the minimum intensity of sound audible to the average person, or 1.0 x 10^-12 W/m^2.
a) The sound intensity at a concert is measured to be 0.9 W/m^2. How loud is the concert?
My answer (that is correct); 119.54 dB
b) At the concert, the person beside you whispers with a loudness of 20 dB. What is the whisper's intensity?
My attempt: (but it is wrong)
20+119.54=10log(I/10^-12)
Then I solved for I, to get T=89
c) On the way home from the concert, your car stereo produces 120 dB of sound. What is its intensity?
I did not get this answer either, but tried to do it like b...
Help on parts b and c please!
To solve part b, you need to rearrange the equation L=10log(I/I_o) to solve for I. Here's how you can do it step by step:
1) Start with the equation: L = 10log(I/I_o)
2) Divide both sides of the equation by 10: L/10 = log(I/I_o)
3) Rewrite the equation in exponential form: 10^(L/10) = I/I_o
4) Multiply both sides of the equation by I_o: I = I_o * 10^(L/10)
Now you can plug in the given loudness of 20 dB and the minimum intensity I_o:
I = (1.0 x 10^-12 W/m^2) * 10^(20/10)
Simplifying further:
I = (1.0 x 10^-12 W/m^2) * 10^2
I = (1.0 x 10^-12 W/m^2) * 100
I = 1.0 x 10^-10 W/m^2
Therefore, the intensity of the whisper is 1.0 x 10^-10 W/m^2.
Now let's move on to part c:
Using the same rearranged equation, you can find the intensity for a given loudness of 120 dB:
I = I_o * 10^(L/10)
Substituting the values:
I = (1.0 x 10^-12 W/m^2) * 10^(120/10)
Simplifying further:
I = (1.0 x 10^-12 W/m^2) * 10^12
I = (1.0 x 10^-12 W/m^2) * 1,000,000,000,000
I = 1.0 x 10^0 W/m^2
Since 10^0 is equal to 1, the intensity of the sound from the car stereo is 1.0 W/m^2.
Therefore, the intensity of the car stereo is 1.0 W/m^2.