Answer
a) If two of the same dogs were barking, the intensity level would be between 40 dB and 80 dB.
When two sound sources of the same intensity are combined, the resulting intensity level is increased by 3 dB. So, if one dog's bark has an intensity level of 40 dB, and a second identical dog barks at the same time, the resulting intensity level would be:
$IL_{total} = IL_1 + 3 dB$
$IL_{total} = 40 dB + 3 dB = 43 dB$
This intensity level is between 40 dB and 80 dB, so the correct answer is option (2).
(b) The intensity of the sound from two dogs barking can be calculated using the formula:
$IL_{total} = 10 log\frac{I_{total}}{ I_{ref}} $
where IL_total is the intensity level of the combined sound, I_total is the total sound intensity, and I_ref is the reference intensity (1 x 10^-12 W/m^2).
We can use the fact that the change in intensity level when two sound sources of the same intensity are combined is 3 dB to calculate the total intensity of the two barking dogs:
$IL_{total} = IL_{1} + 3 dB = 40 dB + 3 dB = 43 dB$
We can convert this intensity level to intensity using the formula:
$ I_{total} = I_{ref} * 10^{\frac{IL_{total}}{10}}$
$I_{total} = (1 x 10^-12 W/m^2) * 10^{\frac{43}{10}}$
$I_{total} = 1.00 x 10^-7 W/m^2 $
So the intensity of the sound from two dogs barking is 1.00 x 10^-7 W/m^2.
Work Step by Step
a) If two of the same dogs were barking, the intensity level would be between 40 dB and 80 dB.
When two sound sources of the same intensity are combined, the resulting intensity level is increased by 3 dB. So, if one dog's bark has an intensity level of 40 dB, and a second identical dog barks at the same time, the resulting intensity level would be:
$IL_{total} = IL_1 + 3 dB$
$IL_{total} = 40 dB + 3 dB = 43 dB$
This intensity level is between 40 dB and 80 dB, so the correct answer is option (2).
(b) The intensity of the sound from two dogs barking can be calculated using the formula:
$IL_{total} = 10 log\frac{I_{total}}{ I_{ref}} $
where IL_total is the intensity level of the combined sound, I_total is the total sound intensity, and I_ref is the reference intensity (1 x 10^-12 W/m^2).
We can use the fact that the change in intensity level when two sound sources of the same intensity are combined is 3 dB to calculate the total intensity of the two barking dogs:
$IL_{total} = IL_{1} + 3 dB = 40 dB + 3 dB = 43 dB$
We can convert this intensity level to intensity using the formula:
$ I_{total} = I_{ref} * 10^{\frac{IL_{total}}{10}}$
$I_{total} = (1 x 10^-12 W/m^2) * 10^{\frac{43}{10}}$
$I_{total} = 1.00 x 10^-7 W/m^2 $
So the intensity of the sound from two dogs barking is 1.00 x 10^-7 W/m^2.
