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!
b,
20=10log(I/Io)
I/Io=antilog2=100
so I is 100 times (Io)
c.
120=10log(I/Io)
I/Io=antilog 12=10^12
b) To find the whisper's intensity, we can rearrange the equation L=10log(I/I_o) to solve for I:
L = 20 dB
I_o = 1.0 x 10^-12 W/m^2
L = 10log(I/I_o)
2 = log(I/I_o)
10^2 = I/I_o
100 = I/I_o
Therefore, the whisper's intensity is 100 times the minimum audible intensity:
I = 100 x I_o
I = 100 x 1.0 x 10^-12 W/m^2
I = 1.0 x 10^-10 W/m^2
So, the whisper's intensity is 1.0 x 10^-10 W/m^2.
c) Similar to part b, we can solve for the intensity I using the equation L = 10log(I/I_o):
L = 120 dB
I_o = 1.0 x 10^-12 W/m^2
L = 10log(I/I_o)
12 = log(I/I_o)
10^12 = I/I_o
Therefore, the stereo's intensity is 10^12 times the minimum audible intensity:
I = 10^12 x I_o
I = 10^12 x 1.0 x 10^-12 W/m^2
I = 1.0 W/m^2
So, the stereo's intensity is 1.0 W/m^2.
To find the answers to parts b and c, let's use the equation L = 10log(I/I_o), where L is the loudness in decibels, I is the intensity in watts per square meter, and I_o is the minimum intensity of sound audible to the average person (1.0 x 10^-12 W/m^2).
For part b, we need to find the intensity (I) when the loudness (L) is equal to 20 dB. We can rearrange the equation to solve for I:
L = 10log(I/I_o)
20 = 10log(I/1.0 x 10^-12)
Dividing both sides by 10:
2 = log(I/1.0 x 10^-12)
To remove the logarithm, we need to raise both sides of the equation to the power of 10:
10^2 = I/1.0 x 10^-12
Simplifying:
100 = I / 1.0 x 10^-12
We can multiply both sides by 1.0 x 10^-12 to isolate I:
100 * 1.0 x 10^-12 = I
1.0 x 10^-10 = I
So, the intensity of the whisper is 1.0 x 10^-10 W/m^2.
For part c, we need to find the intensity (I) when the loudness (L) is equal to 120 dB. Following a similar approach:
L = 10log(I/I_o)
120 = 10log(I/1.0 x 10^-12)
Dividing both sides by 10:
12 = log(I/1.0 x 10^-12)
Raising both sides to the power of 10:
10^12 = I/1.0 x 10^-12
Simplifying:
10^12 = I / 1.0 x 10^-12
We can multiply both sides by 1.0 x 10^-12 to isolate I:
1.0 x 10^-12 * 10^12 = I
1.0 W/m^2 = I
So, the intensity of the car stereo is 1.0 W/m^2.
Therefore, the answers to parts b and c are:
b) The whisper's intensity is 1.0 x 10^-10 W/m^2.
c) The car stereo's intensity is 1.0 W/m^2.