A sound wave travels out uniformly in all directions from a point source. (a) Wh

Question

A sound wave travels out uniformly in all directions from a point source. (a) Which of the following expressions is that for the displacement s of the transmitting medium at any distance r from the source, where b is a constant? Consider the speed, direction of propagation, periodicity, and intensity of the wave. (b) What is the dimension of the constant b?

a)s=(b/r)*sin(kr+wt)+(b/r)cos(kr-wt)

b)s=(b/(r^3))*sin(kr-wt)

c)s=b*cos(kr+wt)

d)s=(b/r)*cos(kr-wt)

b)m^-2, m^-1, m^2, m^3

d)s=(b/r)*cos(kr-wt)

Explanation / Answer

None of the given expressions looks correct.

The correct one has to be:

s = b/r sin(kr - wt)

We know that, intensity = power/area = P/4 pi r^2

since, intensity is proportional to area^2, we can write

I = Cs^2 => P/4 pi r^2 = Cs^2

s = sqrt (P/4 pi r^2C) = 1/ r sqrt (P/4 pi C)

s is inversely prop to r

s = 1/r sqrt (P/4 pi C) sin(kr - wt) = b/r sin(kr - wt)

where b = sqrt (P/4 pi C)

b)dimension of b will be m^2

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