Question

Sound intensity varies inversely as the square of the distance from the sound source. If youare in a movie theater and you change your seat to one that is thrice as far from thespeakers, how does the new sound intensity compare with that of your original seat?The sound intensity is of what it was originally.(Type an integer or a fraction.)

Answer 1

Let the initial intensity be I, then,

`I=(x)/(d^2)`

Here, x is the proportionality constant and d is the distance.

When the seat is changed o one that is thrice as far from the

speakers, we have the new intensity as,

`I^(\prime)=(x)/((3d)^2)=(x)/(9d^2)`

Therefore, the new intensity in terms of the original intensity can be written as,

`I^(\prime)=(x)/(9d^2)=(1)/(9)* I`

Thus, the required fraction is 1/9.