Question

4. Given a cubical room 10 ft on a side,

   1. What is the mean free path of a sound ray in the room?
   2. How many reflections per second does an average ray make with the walls?
   3. If the loss in level per reflection is 1.5 dB, what are the reverberation time for the room and the average absorptivity of the walls?

Answer 1

(a) approximate mean free path between reflections in a compact room m = 4V/S (ft)

here, S = room total surface area (sq ft), V = room volume (cu ft),

s = 6a^2 = 6 x 10 x 10 = 600 sq. ft.

V = a^3 = 10 x 10 x 10 = 1000 cu. ft.

so, m = 4x (1000) / 600 = 6.66 .

(b)

average reflection rate: R = (distance traveled in 1 sec, i.e. velocity of sound)/(average distance between reflections, i.e. mean free path)

R = 1130 ft/sec / 6.66 = 169.5 reflections / sec. Ans.

(c)

reverberation time: for a 1.5 dB decay, the time required will be T = 1.5/r .

here.

average decay rate: r = (average reflection rate)(average decay per reflection)

r = Rd = (169.5) 10 log (1/(1 - a)) here a = absoption coefficient (Not given).