Sound from a 55dB horn is measured at a distance. What is the intensity of the sound in W/m2?
To calculate the intensity of sound in W/m², we need the sound level in decibels (dB) and the reference sound level of 0 dB, which corresponds to an intensity of 1 x 10^-12 W/m².
The formula to convert from dB to intensity in W/m² is:
I = 10^((L - L₀)/10)
Where:
I is the intensity in W/m²,
L is the sound level in dB,
L₀ is the reference sound level in dB.
In this case, the sound level is 55 dB. The reference sound level is 0 dB.
Plugging the values into the formula:
I = 10^((55 - 0)/10)
I = 10^(55/10)
I = 10^(5.5)
Calculating the value:
I ≈ 316.227766 W/m²
Therefore, the intensity of the sound from the 55 dB horn is approximately 316.23 W/m².
To find the intensity of a sound in W/m², you'll need to use the formula:
I = (10^(dB/10)) * I₀
Where:
- I is the intensity of the sound in W/m²
- dB is the sound level, in this case, 55 dB
- I₀ is the reference intensity, which is 1 * 10^(-12) W/m²
Let's plug in the values and calculate it step by step:
dB = 55
I₀ = 1 * 10^(-12) W/m²
I = (10^(55/10)) * (1 * 10^(-12))
I = 10^(5.5) * (1 * 10^(-12))
I = 31622.7766 * (1 * 10^(-12))
I = 3.16227766 * 10^(-8) W/m²
Therefore, the intensity of the sound from the 55 dB horn at a distance is approximately 3.16227766 × 10^(-8) W/m².
1 W/m² is defined as 120 dB.
For every 10 dB higher, power is multiplied by 10 times.
Inversely, for every 10 db lower, power is reduced (divided) by 10 times.
For example,
100 db = (120-20) dB=1W/m²*10^-2
75 dB = (120-45) dB = 1W/m²*10^(-4.5)=10^(-4.5) W/m²
You can work out 55dB in W/m² similarly.
Also, read the following link for more information.
http://www.physicsclassroom.com/class/sound/Lesson-2/Intensity-and-the-Decibel-Scale