Question

Five people talk simultaneously. If the intensity level is 70 dB when either one speaks alone, what is the intensity level when both speak at once?

Answer 1

a) Intensity from 1 person = i, from 5 people = 5i, reference level = iₒ
dB = 10 log (i / iₒ)

For 1 person .. 97 = 10 log (i/iₒ) .. log (i/iₒ) = 9.7 .. i /iₒ = 10^9.7 .. .. i = iₒ x 10^9.7

For 5 people .. i' = 5 i .. .. i' = 5 iₒ x 10^9.7..
dB = 10 log (i' / iₒ)
dB = 10 log (5 iₒ x 10^9.7 / iₒ)
dB = 10 log (5 x 10^9.7) .. 10 log (5 x 5.01^9) .. 10 log (2.506^10) .. 10 x 10.39

Total intensity ►= 104 dB .. .. (103.9 dB)

b)
F' = frequency that arrives at insect (source [Vs] moving towards insect)
F'= Vo x Fo / (Vo - Vs)
F' = 340m/s x 60.60kHz / (340m/s - 4.70m/s) .. .. F' = 61.45 kHz

F'' = frequency received by bat moving [Vr] towards stationary source F' (reflected by insect)
F'' = (Vo + Vr)F' / Vo
F'' = (340 + 4.70) x 61.45kHz / 340 .. .. .. ►F'' = answer 62.30 kHz