I've done a similar problem to this before, only it included speakers and the problem specifically stated that the sound spread out spherically. So I'm not sure if I'm always supposed to assume that it spreads spherically?

An express commuter train passes a station at full speed while sounding its horn. A person standing on the platform hears a sound level of 90dB when the train’s horn is 10m away. How far away will the train be when its sound level is 50dB? Assume the horn is a point source.


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There are many reasons why the answer to this question is quite complicated - but I am pretty sure that you are expected to treat the propagation of the sound as though it's spherical (I deduce this from the "assume the horn is a point source" instruction).

The fact that the train is probably running on the ground means that you really only have a hemisphere of sound; then there is the (frequency-dependent) attenuation of sound in air, and diffraction effects... ignore all of those.

So treat it like an inverse square problem. Double the distance, lose 6 dB. Going from 90 dB to 50 dB you lost 6 dB 40/6 times.

You can figure out the rest.


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