How to find the total dB of two sounds?

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In summary, the total loudness when the turned-off speaker is turned back on is 71.5dB. This is calculated by taking the original loudness of 70dB and adding 1.5dB, which is found by taking the square root of 2 and using the equation for dB, 10log(I/I0). This is because intensity is proportional to the root of amplitude.
  • #1
Summer95
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Homework Statement


The frequency of the two sounds is the same, and the observer is equal distance from either sound source. When one speaker is turned off the loudness is 70dB, what is the total loudness when it is turned back on?

Homework Equations


A2∝I
dB=10log(I/I0)

The Attempt at a Solution


$$10log(\sqrt{\frac{2A}{A}})=10log\sqrt{2}=1.5$$
and 70+1.5=71.5dB

but I do not see it done this way anywhere so I don't know what I'm doing wrong
 
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  • #2
Intensity is amplitude squared, not the other way round. Where does the square root come from?
 
  • #3
The square root comes from the equation for dB which is 10log(I/I0)

But if you are doubling the amplitude that part becomes √2 right?
 
  • #4
Summer95 said:
The square root comes from the equation for dB which is 10log(I/I0)

But if you are doubling the amplitude that part becomes √2 right?
because Intensity is proportional to the root of amplitude.
 
  • #5
Summer95 said:
because Intensity is proportional to the root of amplitude.
nevermind your right I had it the wrong way round
 

1. What is dB and why is it used to measure sound?

dB (decibel) is a unit of measurement used to quantify the amount of sound energy in a signal. It is used because it allows for a more accurate and consistent measurement of sound levels, compared to other units like loudness or volume.

2. How do you calculate the total dB of two sounds?

To find the total dB of two sounds, you must first convert each sound's intensity level (measured in dB) to its corresponding sound pressure level (measured in pascals). Then, you can use the formula Ltotal = 10log10 (10^(L1/10) + 10^(L2/10)), where L1 and L2 are the sound pressure levels of the two sounds. This will give you the total sound pressure level, which can be converted back to dB if needed.

3. Can two sounds with the same dB level have a different total dB?

Yes, two sounds with the same dB level can have a different total dB. This is because the total dB takes into account the combined sound pressure level of the two sounds, which can vary depending on the frequencies and intensities of each sound.

4. How do distance and direction impact the total dB of two sounds?

The distance and direction of the sounds can impact the total dB by affecting the sound pressure levels of each sound. As sound travels, it spreads out and loses energy, resulting in a decrease in sound pressure level. The direction of the sounds can also affect how they combine, resulting in a different total dB.

5. What is the maximum total dB that can be reached by combining two sounds?

The maximum total dB that can be reached by combining two sounds is 3 dB higher than the loudest of the two individual sounds. This is known as the "3 dB rule" and is due to the logarithmic nature of decibels.

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