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Get Full Access to University Physics - 13 Edition - Chapter 16 - Problem 9e
Get Full Access to University Physics - 13 Edition - Chapter 16 - Problem 9e

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# Unless indicated otherwise, assume the speed of | Ch 16 - 9E

ISBN: 9780321675460 31

## Solution for problem 9E Chapter 16

University Physics | 13th Edition

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Problem 9E

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. An oscillator vibrating at 1250 Hz produces a sound wave that travels through an ideal gas at 325 m/s when the gas temperature is 22.0o C. For a certain experiment, you need to have the same oscillator produce sound of wavelength 28.5 cm in this gas. What should the gas temperature be to achieve this wavelength?

Step-by-Step Solution:

Solution 9E Step 1: In this question we need to find the temperature of gas to achieve wavelength 28.5 m/s Consider the data given Frequency f = 1250 Hz Speed of the wave v = 352 m/s Temperature of the gas T 1 22 + 273 = 295 K Wavelength needed = 28.5 cm 2 RT v = M Here = ratio of heat capacity = 1.40 R = gas constant = 8.314 J /mol 3 M = molar mass of gas = 28.8 × 10 kg /mol Rearranging the equation to find T we get M 2 T = (R v Substitute v=344 m/s We get 3 T = ( 28.8×10 ) × (325 m/s )2 1.40×8.314 J/mol T = 354.4 K Thus we have temperature in degree as 354.4 273 = 81.4 0 Hence the temperature of the gas to have wavelength is 28.5 is 81.4 C

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