How Does Sound Intensity Change with Multiple Instruments?

[glasshut137]

Homework Statement

The average sound level of a typical musical instrument in a musical group is B dB. WHat is the sound level in Db if 10 instruments are simultaneously playing.

answer choices: B'= 10B, 5B, B+5, B+20, B+2, B+10, B+1, 20B, B, or 2B

My first thought was that it would be 10B since each instrument would contribute a sound level of B. My logic seems too simple. Can someone tell me if I'm on the right path? thanks.

 

[alphysicist]

Hi glasshut137,

When you have multiple sound sources, the total sound level in dB does not add (so two 10dB sources do not give a sound level of 20dB). Instead it is the intensity of the sound that adds together.

You should have an expression that relates sound level in dB and sound intensity so that you can convert from one to the other and back. What do you get?

 

[Moetasim]

Yes, you are on the right path. The sound level in dB is logarithmically proportional to the intensity of the sound, so if 10 instruments are playing simultaneously, the overall sound level would be 10 times the sound level of a single instrument. Therefore, the correct answer is B' = 10B. This is because the sound levels would add up, rather than being multiplied, so it would not be 20B or 2B. The other answer choices do not accurately reflect the increase in sound level when multiple instruments are playing.