A loudspeaker has an output of 65 dB. If the volume of the sound is turned up so that the output intensity is?

Question

A loudspeaker has an output of 65 dB. If the volume of the sound is turned up so that the output intensity is 5000 times greater, what is the new sound intensity level?

Iam having trouble with the dB, iam not to sure what number to add to 65

Answer 1

Well, you are talking about increase volume level (loudness) over that of 65 dB.  Of course you would want to use the power formula for power gain in dB.

dB = 10 x log (Po / Pin)

Since we are talking about an increase of intensity of 5000 times, that's going to be an increase over 65 dB.

Let 65 dB = unity or 1.0, for Pin; let Po = 5000 times Pin

Thus,  X dB = 10 x log (5000 / 1.0)

X dB = 37 ; thus, this is a 37 dB increase over the original 65 dB.   65 dB + 37 dB = 102 dB total

Now, I'm pretty sure that's right but not absolutely certain.

Answer 2

five times 1000 times the intensity is

7 dB for the 5 times

30 dB for the 1000 times

so 37dB + 65 dB = 102dB