Question

Loudspeakers can produce intense sounds with surprisingly small energy input in spite of their low efficiencies. Calculate the power input needed (in W) to produce a 92.1 dB sound intensity level for a 15.5 cm diameter speaker that has an efficiency of 1.06%. (This value is the sound intensity level right at the speaker.)

Answer 1

Sound intensity level right at the speaker = = 92.1 dB

Sound intensity right at the speaker = I

I = 1.622 x 10^-3 W/m²

Diameter of the speaker = D = 15.5 cm = 0.155 m

Area of the speaker = A

A = 1.887 x 10^-2 m²

Power output of the speaker = P_out

P_out = IA

P_out = (1.622x10^-3)(1.887x10^-2)

P_out = 3.061 x 10^-5 W

Power input to the speaker = P_in

Efficiency of the speaker = = 1.06% = 0.0106

P_in = 2.89 x 10^-3 W

Power input needed by the speaker = 2.89 x 10^-3 W