The loudness L in decibels, the intensity of the sound I, and the minimum intensity of sound detectable by human ear m, are related by the equation L=10log( Im).
B
b
The loudness L in decibels, the intensity of the sound I, and the minimum intensity of sound detectable by human ear m, are related by the equation L=10log( Im).
A
a
The noise level of car with the old muffler is 10^(8.5)≈ 316 227 766 times the minimum intensity of sound detectable by the human ear.
B
b
The noise level of car with the old muffler is 10^(7.3)≈ 19 952 623 times the minimum intensity of sound detectable by the human ear. The percent of decrease of the intensity of sound detectable by human ear is about 93.7 %.
Practice makes perfect
a
The loudness L in decibels, the intensity of the sound I, and the minimum intensity of sound detectable by human ear m, are related by the following equation.
L=10log( Im)
We are asked to find how many times the minimum intensity of sound detectable by the human ear was the car with the old muffer, if m is defined by 1. Furthermore, we know that the loudness of the old muffler was 85 decibels. Let's substitute the known values and find I.
To solve the equation for I, we will use the definition of a logarithm. Notice also that log x is equal to log_(10)x for all x.
y=log_b x ⇔ x= b^y
This definition tells us how to rewrite the logarithm equivalent of y as an exponential equation. The argument x is equal to b raised to the power of y. Let's do it!
8.5=log_(10) I ⇔ I= 10^(8.5)
Finally, using a calculator, we get that I=10^(8.5)≈ 316 227 766.
b
The loudness L in decibels, the intensity of the sound I, and the minimum intensity of sound detectable by human ear m, are related by the following equation.
L=10log( Im)
We are asked to find how many times the minimum intensity of sound detectable by the human ear was the car with the new muffer, if m is defined by 1. Furthermore, we know that the loudness of the new muffler is 73 decibels. Let's substitute the known values and find I.
To solve the equation for I, we will use the definition of a logarithm. Notice also that log x is equal to log_(10)x for all x.
y=log_b x ⇔ x= b^y
This definition tells us how to rewrite the logarithm equivalent of y as an exponential equation. The argument x is equal to b raised to the power of y. Let's do it!
7.3=log_(10) I ⇔ I= 10^(7.3)
Finally, using a calculator, we get that I=10^(7.3)≈ 19 952 623.
The Percent of Decrease
We want to find the percent of decrease of the intensity of the sound with the new muffler. Let's recall that the loudness of the old muffler is 316 227 766, and the new muffler is 19 952 623. Let's find the decrease in loudness from the old to the new muffler.
