Question

Two people hear a tornado siren, but one listener is 44.1 times farther away from the source of the sound than the other. What is the intensity level (in dB) at the farther listener relative to the other listener?

Answer 1

From the inverse square law, increasing the distance by 44.1 times reduces the intensity by 44.1^2 = 1944.81times.

The intensity level (in dB) at the farther listener relative to the other listener is:

= 10log(ratio of intensities)

= 10log(1/1944.81)

= 10log(0.000514)

=

= -32.89dB (note the negative sign,as the sound is less intense for the farther listener)

Answer 2

Answer 3

From the inverse square law, increasing the distance by 44.1 times reduces the intensity by 44.1^2 = 1944.81 times.

The intensity level (in dB) at the farther listener relative to the other listener is:
= 10log(ratio of intensities)
= 10log(1/1944.81)
= 10log(0.007305)
= 10 x -3.28
= -32.8dB (note the negative sign,as the sound is less intense for the farther listener)

Answer 4

https://skydrive.live.com/redir?resid=D01CE62B7C46ED0C%21908

Answer 5

Intensity levels can be compared on a logarithmic scale as

$$\mathit{\beta }=\left(10\text{ dB}\right)\log \left(\frac{I_2}{I_1}\right)$$

Any type of quantity can be compared on a decibel scale, but for now, you are comparing the intensities of two sounds. The intensity ?$I$ of a sound is just the power emitted by the source divided by the surface area over which the sound has spread.

$$I=\frac{P}{A}=\frac{P}{4\mathit{\pi }{r}^2}$$

For a uniformly emitting source, the appropriate surface area is that of a sphere centered on the source. The quantity ?$r$ is the distance of the listener from the source of the sound. The fact that one listener is 27.9$27.9$ times farther away than the other gives the ratio of their distances from the source.

$$\frac{r_2}{r_1}=27.9$$

To calculate the intensity-level difference, you must find the ratio of the two intensities. Solving the intensity relationship for power gives

$$P=4\mathit{\pi }{r}^{2}I$$

Both listeners are hearing the same source, so this relationship may be written equivalently in terms of either listener's variables.

$$P=4\mathit{\pi }{r}_1^2{I}_1=4\mathit{\pi }{r}_2^2{I}_2$$

Solving for the ratio of intensities and using the given ratio of distances leads to

$$\begin{array}{rl}\frac{I_2}{I_1}& =\frac{4\mathit{\pi }{r}_1^2}{4\mathit{\pi }{r}_2^2}\\ & ={\left(\frac{r_1}{r_2}\right)}^2\\ & =\frac{1}{{\left(27.9\right)}^2}\end{array}$$

So, the intensity-level difference in decibels is

?=(10 dB)log(?2?1)=(10 dB)log(1(27.9)2)=−28.912 dB