Recap of last lecture change resisting inertia force restoring v = ρ B v fluid = ρ Y v solid = M RT v gas γ = Applications such as sonar, ultrasonic imaging, ultrasonic surgery Intensity = <Power> av /area = ½B ϖ kA 2 = ½ √B√ ρϖ 2 A 2 = ½ P 2 max /√B√ ρ β = (10dB)log(I/I0 ) where I0 = 1x10-12 W/m 2 (I0 threshold for human hearing at 1000Hz)
Problem 16.55 A soprano and a base are singing a duet. While the soprano sings a A # at 932 Hz the base sings a A # but 3 octaves lower. In this concert hall the density of air is 1.2 kg/m 3 and its bulk modulus is 1.42x10 5 Pa. In order for their notes to have the same sound intensity level, what must be a) the ratio of the pressure amplitude of the bass to that if the soprano, and b) the ratio of the displacement amplitude of the bass to that of the soprano? c) What displacement amplitude does the soprano produce to sing her A # at 72dB?
Problem 16.55 Each octave lower corresponds to halving of the frequency. If the Soprano sings at 932 Hz the Bass must be 932/8 =116.5Hz
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