Question

A bagpiper is playing in the middle of the quad. To a person standing 20 m away, the sound intensity level of the bagpiper is 87.8 dB.

17. What is sound intensity level 25.5 m away from the bagpiper? (Assume that the bagpiper is a point source of spherical waves.)

18. [2pt] What's the intensity of the sound of the bagpiper 25.5 m away?

19. [2pt] If the sound intensity level of one bagpiper is 87.8 dB twenty meters away, How many bagpipers would you need to produce 119.998 dB at this distance?

Answer 1

Let the energy radiated per unit time (power) from bag piper is S watt so intensity of sound at rr_1 distance is I_1 = s/4 pi rr_1^2 (rr_1 = 20 m) Similarly intensity of sound at r_2 distance is I_2 = s/4 pi r_2^2 (rr_2 = 25.5 m) Therefore I_1/I_2 = (rr_2/rr_1)^2 The sound intensity level at r_2 distance is, dB_2 = 10 log I_2/I_0 \r\n 17) dB_2 - dB_1 = 10 log I_2/I_0 - I_0 log I_1/I_0 Rightarrow dB_2 - dB_1 = 10 log I_2/I_1 times I_0/I_1 Rightarrow dB_2 - dB_1 = 10 log I_2/I_1 = log (n_1/n_2)^2 Rightarrow dB_2 = dB_1 - 20 log n_2/n_1 In this case, n_1 = 20 m, n_2 = 25.5 m: dB_1 = 8.78dB Therefore dB_2 = (87.8 - 20 log 25.5/20) dB = (87.8 - 2.11) dB = 85.69 dB so, the sound intensity level at 25.5 m is 85.69 dB