The sound intensity at a person’s seat in a concert hall is 8.010–5 W m–2. Calculate thesound intensity level, in decibels, at the seat. (Use 1.010–12 W m–2 as the reference level.)
Question
The sound intensity at a person’s seat in a concert hall is 8.010–5 W m–2. Calculate thesound intensity level, in decibels, at the seat. (Use 1.010–12 W m–2 as the reference level.)
Solution
To calculate the sound intensity level in decibels, we use the formula:
L = 10 log (I/I0)
where: L is the sound level in decibels, I is the intensity of the sound wave, and I0 is the reference intensity.
Given in the problem, I = 8.0 x 10^-5 W/m^2 and I0 = 1.0 x 10^-12 W/m^2.
Substituting these values into the formula, we get:
L = 10 log (8.0 x 10^-5 / 1.0 x 10^-12)
Solving this, we get:
L = 10 log (8.0 x 10^7)
Using the property of logarithms that log (a*b) = log(a) + log(b), we can simplify this to:
L = 10 [log (8.0) + log (10^7)]
Since log (10^7) = 7, this simplifies to:
L = 10 [log (8.0) + 7]
Finally, calculating log (8.0) approximately equals to 0.9031, we get:
L = 10 [0.9031 + 7]
L = 10 * 7.9031
L = 79.031 dB
So, the sound intensity level at the person's seat in the concert hall is approximately 79 dB.
Similar Questions
Decibels measure sound(a) intensity(b) frequency(c) loudness level(d) all of the above (8.5)
The sound of a band is rated as 60 dB at a distance of 10.0 m. What is the sound intensity level of the band when one is 20.0 m from the band?
Select the correct answer from the drop-down menu.The formula 𝛽=10log(𝐼𝐼0) is used to find the sound level, 𝛽 , in decibels (dB), of a sound with an intensity of I. In the formula, 𝐼0 represents the smallest sound intensity that can be heard by the human ear (approximately 10-12watts/meter2 ).The sound level on a busy street is 70 dB. What is the sound intensity on the street?The sound intensity on the busy street is watts/meter2 .
8. Sound Intensity The table lists intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity. Sound Intensity Scale Value 316 25.0 500 27.0 750 28.75 2000 33.0 5000 37.0
If the intensity of a sound wave is 10 W/m² at a distance of 5 m from the source, calculate the intensity at a distance of 20 m from the source.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.