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# A soprano and a bass are singing a duet. While the soprano ISBN: 9780321675460 31

## Solution for problem 59P Chapter 16

University Physics | 13th Edition

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Problem 59P

A soprano and a bass are singing a duet. While the soprano sings an A-sharp at 932 Hz, the bass sings an A-sharp but three octaves lower. In this concert hall, the density of air is 1.20 kg/m and its bulk modulus is 1.42 X 105 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 of the soprano and (b) the ratio of the displacement amplitude of the bass to that of the soprano? (c) What displacement amplitude (in m and in nm) does the soprano produce to sing her A-sharp at 72.0 dB?

Step-by-Step Solution:

Solution 59P Problem (a) To find the ratio of pressure amplitude Step 1: Frequency of Soprano f = 932 Hz 1 Density of air = 1.2 kg/m 3 5 Bulk modulus B = 1.42x10 Pa The intensity level is same Step 2: Pmaxb Ib = 2B Is P maxs 2B Where I s - Intensity of soprano Ib- Intensity of bass Here density of air and bulk modulus are constants. They cancel each other. The Intensity is same for both soprano and bass Step 3: Therefore 1 = P maxb P maxs P maxs = P maxb The ratio of Pressure amplitude of bass to the soprano = 1 Problem (b) To find the ratio of displacement amplitude of bass to that of soprano Step 1: Frequency of Soprano f s = 932 Hz Frequency of bass is 3 octave lower than the soprano 3 3 Frequency of Bass f b = f s2 = 932*2 Frequency of Bass f b = 116.5 Hz Step 2: B.A.2.f I = v v - velocity of sound B, v are constants The ratio of intensity is same Step 3: Cancelling constants and substituting Intensity value I A f I b = A fb s s s A b*16.5 1 = A *932 A b 932 A s = 116.5 A b = 8 A s ratio of displacement amplitude of bass to that of soprano = 8 Problem (c) Step 1: To find displacement amplitude Intensity level = 72dB Before finding displacement amplitude, we must find intensity and pressure amplitude. Step 2: Intensity I = I .10 /10 0 12 72/10 I = 10 .10 I = 1012.107.2 I = 1.58x10 5 W/m 2

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##### ISBN: 9780321675460

This full solution covers the following key subjects: soprano, Bass, amplitude, sharp, sings. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “A soprano and a bass are singing a duet. While the soprano sings an A-sharp at 932 Hz, the bass sings an A-sharp but three octaves lower. In this concert hall, the density of air is 1.20 kg/m and its bulk modulus is 1.42 X 105 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 of the soprano and (b) the ratio of the displacement amplitude of the bass to that of the soprano? (c) What displacement amplitude (in m and in nm) does the soprano produce to sing her A-sharp at 72.0 dB?” is broken down into a number of easy to follow steps, and 113 words. Since the solution to 59P from 16 chapter was answered, more than 1336 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 59P from chapter: 16 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This textbook survival guide was created for the textbook: University Physics, edition: 13.

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