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Chapter 16: Problem 23

The density of a sample of air is \(1.205 \mathrm{~kg} / \mathrm{m}^{3}\), and the bulk modulus is \(1.42 \cdot 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) a) Find the speed of sound in the air sample. b) Find the temperature of the air sample.

Short Answer

Expert verified
Answer: The speed of sound in the air sample is approximately 331.25 m/s, and the temperature is approximately 273.1 K.

Step by step solution

01

Find the speed of sound in the air sample

To find the speed of sound in the air sample, we will use the following formula: v = sqrt(B/ρ) Where v is the speed of sound, B is the bulk modulus, and ρ is the density. Given values: B = 1.42 * 10^5 N/m^2 ρ = 1.205 kg/m^3 Plug in the given values into the formula: v = sqrt((1.42 * 10^5 N/m^2) / (1.205 kg/m^3)) Now, calculate the speed of sound (v): v ≈ 331.25 m/s The speed of sound in the air sample is approximately 331.25 m/s.
02

Find the temperature of the air sample

To find the temperature of the air sample, we will use the following formula: v = sqrt(γRT / ρ) Where v is the speed of sound, γ is the adiabatic index, R is the specific gas constant for air, T is the temperature, and ρ is the density. Given values: v = 331.25 m/s γ = 1.4 (adiabatic index for air) R = 287 J/(kg*K) (specific gas constant for air) ρ = 1.205 kg/m^3 Rewrite the formula to isolate T: T = (v^2 * ρ) / (γR) Plug in the known values into the formula: T = ((331.25 m/s)^2 * (1.205 kg/m^3)) / (1.4 * 287 J/(kg*K)) Now, calculate the temperature (T): T ≈ 273.1 K The temperature of the air sample is approximately 273.1 K.

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Most popular questions from this chapter

You are standing between two speakers that are separated by \(80.0 \mathrm{~m}\). Both speakers are playing a pure tone of \(286 \mathrm{~Hz}\). You begin running directly toward one of the speakers, and you measure a beat frequency of \(10.0 \mathrm{~Hz}\). How fast are you running?

When two pure tones with similar frequencies combine to produce beats, the result is a train of wave packets. That is, the sinusoidal waves are partially localized into packets. Suppose two sinusoidal waves of equal amplitude A, traveling in the same direction, have wave numbers \(\kappa\) and \(\kappa+\Delta \kappa\) and angular frequencies \(\omega\) and \(\omega+\Delta \omega\), respectively. Let \(\Delta x\) be the length of a wave packet, that is, the distance between two nodes of the envelope of the combined sine functions. What is the value of the product \(\Delta x \Delta \kappa ?\)

At a distance of \(20.0 \mathrm{~m}\) from a sound source, the intensity of the sound is \(60.0 \mathrm{~dB}\). What is the intensity (in \(\mathrm{dB}\) ) at a point \(2.00 \mathrm{~m}\) from the source? Assume that the sound radiates equally in all directions from the source.

A classic demonstration of the physics of sound involves an alarm clock in a bell vacuum jar. The demonstration starts with air in the vacuum jar at normal atmospheric pressure and then the jar is evacuated to lower and lower pressures. Describe the expected outcome.

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