Answer:
The distance at which the music is just barely audible is 108262.50 m
Explanation:
Sound intensity is the energy transmitted by a source in a unit area. The unit is in decibels.
Recall L2 -L1 = -20 log r2/r1 with the log in base 10
L = sound level in decibels, r =distance from source of sound
the sound becomes barely audible at location 0 decibel , applying this concept
0 - 83.9 = - 20 log r2/6.91
20log r2/6.91 = 83.9
log r2/6.91 = 83.9/20 = 4.195 , applying the laws of logarithms
r2/6.91 = 10^4.195 = 15667.5107
r2 = 6.91 * 15667.5107 = 108262.50 m
Given Information:
Intensity level = 83.9 dB
distance = d1 = 6.91 m
Required Information:
distance where sound is barely audible = d2 = ?
Answer:
d2 = 108262.5 m
Explanation:
As we know the intensity level of sound is
Intensity level = 10*log(I/I₀)
I₀ = 10⁻¹²W/m² is the reference intensity level or threshold
83.9 = 10*log(I/I₀) eq. 1
The intensity of sound and distance are inversely related as
I ≈ 1/d²
At d1 intensity of sound is 83.9 dB
We want to find the distance d2 where intensity of sound is 0 dB so
I₀/I = (d1/d2)²
or I/I₀ = (d2/d1)²
Substitute the ratio of I/I₀ into eq. 1
83.9 = 10*log(d2/d1)²
83.9 = 20*log(d2/d1)
83.9/20 = log(d2/d1)
4.195 = log(d2/d1)
10⁴°¹⁹⁵ = d2/d1
d1*15667.51 = d2
d2 = 15667.51*6.91
d2 = 108262.5 m
Therefore, sound of music will barely be heard at a distance of 108262.5 m from the source of music.
