Question

The psychological sensation of loudness B is measured in decibels and is defined with reference to the intensity, , of a barely audible sound by the following equation. In this equation, I is the intensity of the sound in question.

B=10log 1/1o
If the sound of a jet engine during takeoff is 140 decibels and the sound of a rock concert is 115 decibels, how does the intensity of the sound of the jet engine compare to the intensity of the sound of the rock concert?
I got that the intensity of the concert would be louder...is this right?

Answer 1

check your typing

your equation contains no l
besides that, what is 1o ?

Answer 2

im sorry the 1 is l and the zero is the lower exponet

Answer 3

You mean I think:

Db = 10 log (I/Io)

Answer 4

no, wrong. The higher the Db the louder

140 = 10 log (Ijet/Io)
115 = 10 log (Iband/Io)

14-11.5 = log (Ijet/IIband)

10^2.5 = Ijet/Iband = 316

the jet intensity (power) is 316 times the rock concert

Answer 5

Thanks i see what i did wrong

Answer 6

is it 21?

Answer 7

[AI-generated answer — Explain Bot]

To compare the intensity of the sound of the jet engine to the intensity of the sound of the rock concert, we need to use the equation you provided:

B = 10log(I/1o)

Given that the sound of the jet engine is 140 decibels and the sound of the rock concert is 115 decibels, we can substitute these values into the equation:

For the jet engine:
B1 = 140

For the rock concert:
B2 = 115

Now, we can rearrange the equation to solve for the ratio of intensities, I1/I2:

B1 = 10log(I1/1o)
140 = 10log(I1/1o)

B2 = 10log(I2/1o)
115 = 10log(I2/1o)

Next, we can divide the equations to find the ratio:

(10log(I1/1o))/(10log(I2/1o)) = 140/115

Simplifying the left side:

log(I1/1o)/log(I2/1o) = 140/115

Using logarithm properties, we can rewrite the equation:

log(I1/1o) = log(I2/1o) * 140/115

Now, we can solve for the ratio of intensities:

I1/1o = (I2/1o)^(140/115)

Since the intensities are proportional to the square of the sound intensities, we can square both sides:

(I1/1o)^2 = [(I2/1o)^(140/115)]^2

Now, we can simplify and compare the intensities:

(I1/1o)^2 = (I2/1o)^(280/115)

This means that the intensity of the jet engine (I1) is equal to the intensity of the rock concert (I2) raised to the power of (280/115).

Based on our calculation, the intensity of the jet engine is greater than the intensity of the rock concert. Therefore, the jet engine is louder than the rock concert.