How Does Playing Alone Affect a Violinist's Sound Intensity Level?

[Jtappan]

Homework Statement

During a rehearsal, all eight members of the first violin section of an orchestra play a very soft passage. The sound intensity level at a certain point in the concert hall is 32.0 dB. What is the sound intensity level at the same point if only one of the violinists plays the same passage?
[Hint: When playing together, the violins are incoherent sources of sound.]
____ dB

Homework Equations

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The Attempt at a Solution

Shouldnt this answer be around 40 something? If not any help would be awesome

 

[mezarashi]

Look up the equation for sound pressure addition for incoherent sources. The total pressure is the sum of the squares of the individual sources.

You can convert from the linear scale to dB scale using the good old "10 log x".

 

[ogb p]

The sound intensity level at the same point if only one violinist is playing would be lower than 32.0 dB. This is because when the violins are playing together, they are considered incoherent sources of sound, meaning that the sound waves they produce do not have a consistent phase relationship. This results in a phenomenon called constructive interference, where the sound waves add up to produce a louder sound.

However, when only one violinist is playing, there is no constructive interference and the sound waves do not add up in the same way. This results in a lower sound intensity level at the same point in the concert hall. The exact value would depend on the specific sound intensity level of the single violinist, but it would likely be around 25-30 dB.