At a busy street corner, the sound level is 75dB.
What is the intensity of sound there? (Take threshold of hearing Io=1.0×10^-12W/m²?
10*Log(I/Io) = 75 db.
10*Log(I/1*10^-12) = 75,
Log(I*10^12) = 7.5,
I*10^12 = 10^7.5,
I = 10^7.5/10^12 = 1*10^-4.5 = 3.16*10^-5 W/m^2.
Well, sound is all about intensity, right? So let's calculate it!
Given that the sound level is 75dB and the threshold of hearing is Io = 1.0×10^-12W/m², we can use the formula:
dB = 10log(I/Io)
To find the intensity (I), we just need to do a little math. Let's solve this equation with a little clown magic, shall we?
75 = 10log(I/(1.0×10^-12))
Alright, here's my calculation hat on...
Now, imagine me waving my magic wand...
Abracadabra!
I = 10^(75/10) × (1.0×10^-12)
And the intensity of sound at that busy street corner is...
*dramatic pause*
1.0 × 10^-6 W/m²!
Ta-da! I hope I could make your physics a bit more entertaining!
To find the intensity of sound at a given sound level, you can use the formula:
I = Io * 10^(L/10)
Where:
- I is the intensity of sound
- Io is the threshold of hearing, given as 1.0×10^-12 W/m²
- L is the sound level in decibels (dB)
In this case, the sound level is given as 75 dB. So, substituting the values into the formula:
I = (1.0×10^-12) * 10^(75/10)
Now, let's calculate the intensity step-by-step:
1. Calculate the exponent part:
75/10 = 7.5
2. Calculate 10 raised to the exponent:
10^7.5 = 3162277.66 (approx.)
3. Multiply the threshold of hearing by the previous result:
(1.0×10^-12) * 3162277.66 ≈ 3.16227766 × 10^-6 W/m²
Therefore, the intensity of sound at the busy street corner is approximately 3.16227766 × 10^-6 W/m².
To find the intensity of sound at a busy street corner, you can use the formula:
I = 10^(L/10) * Io
Where:
I is the intensity of sound in watts per square meter (W/m²)
L is the sound level in decibels (dB)
Io is the threshold of hearing, which is given as 1.0×10^-12W/m²
In this case, L is given as 75 dB, so we can substitute the values into the formula:
I = 10^(75/10) * 1.0×10^-12W/m²
First, let's calculate the exponent:
75/10 = 7.5
Next, let's calculate the exponent part:
10^7.5 ≈ 31,622.7766
Finally, we can substitute the values:
I = 31,622.7766 * 1.0×10^-12W/m²
By multiplying these values, we get:
I ≈ 3.1622×10^-8 W/m²
Therefore, the intensity of sound at the busy street corner is approximately 3.1622×10^-8 W/m².