How Does Sound Intensity Change with Fewer Firecrackers?

[Alicek]

Homework Statement

if two firecrackers produce a sound level of 95 dB when fired simultaneously at a certain place, what will the sound level be if only one is exploded?

Homework Equations

dB=10 LOG I + 120

The Attempt at a Solution

would I use 2I instead of I making an equation like 95 = 10 log 2I + 120 and then solve for one I?
Or set up the usual equation and then once I solve for I just divide it in half?
Also, I know that when intensity doubles, it goes up by 3 decibels, so do I just assume that two firecrackers is double the intensity of 1 and just subtract 3 decibels from the original 95?

 

[Redbelly98]

Also, I know that when intensity doubles, it goes up by 3 decibels, so do I just assume that two firecrackers is double the intensity of 1 and just subtract 3 decibels from the original 95?

That's right.

 

[thomate1]

I would approach this problem by first understanding the relationship between decibels and intensity. The equation you provided, dB=10 LOG I + 120, is the correct equation to use. This equation shows that the sound level in decibels is directly proportional to the logarithm of the intensity of the sound.

In this scenario, we have two firecrackers producing a sound level of 95 dB. This means that the combined intensity of the two firecrackers is equal to I.

If we want to find the sound level when only one firecracker is exploded, we can use the same equation and substitute I with half of the original intensity, which is equal to I/2. This gives us:

dB=10 LOG (I/2) + 120

We can simplify this equation to:

dB=10 LOG I - 3 + 120

Since we know that the sound level decreases by 3 decibels when the intensity is halved, we can simply subtract 3 from the original sound level of 95 dB to get the new sound level. This gives us a final answer of 92 dB.

Therefore, if only one firecracker is exploded, the sound level will be 92 dB. It is important to note that this assumes that the two firecrackers have equal intensity and are producing the same sound. If one firecracker is significantly louder than the other, the sound level may not decrease by exactly 3 decibels.