17.8 Shock waves (Page 3/8)

University physics volume 1 Page 3 / 8

Picture is a photograph of the blue glow in a reactor pool. — The blue glow in this research reactor pool is Cerenkov radiation caused by subatomic particles traveling faster than the speed of light in water. (credit: U.S. Nuclear Regulatory Commission)

Summary

The Mach number is the velocity of a source divided by the speed of sound, $M = \frac{v_{s}}{v} .$
When a sound source moves faster than the speed of sound, a shock wave is produced as the sound waves interfere.
A sonic boom is the intense sound that occurs as the shock wave moves along the ground.
The angle the shock wave produces can be found as $sin θ = \frac{v}{v_{s}} = \frac{1}{M} .$
A bow wake is produced when an object moves faster than the speed of a mechanical wave in the medium, such as a boat moving through the water.

Key equations

Pressure of a sound wave	$Δ P = Δ P_{max} sin (k x \mp ω t + ϕ)$
Displacement of the oscillating molecules of a sound wave	$s (x, t) = s_{max} cos (k x \mp ω t + ϕ)$
Velocity of a wave	$v = f λ$
Speed of sound in a fluid	$v = \sqrt{\frac{β}{ρ}}$
Speed of sound in a solid	$v = \sqrt{\frac{Y}{ρ}}$
Speed of sound in an ideal gas	$v = \sqrt{\frac{γ R T}{M}}$
Speed of sound in air as a function of temperature	$v = 331 \frac{m}{s} \sqrt{\frac{T_{K}}{273 K}} = 331 \frac{m}{s} \sqrt{1 + \frac{T_{C}}{273 ° C}}$
Decrease in intensity as a spherical wave expands	$I_{2} = I_{1} {(\frac{r_{1}}{r_{2}})}^{2}$
Intensity averaged over a period	$I = \frac{⟨ P ⟩}{A}$
Intensity of sound	$I = \frac{{(Δ p_{max})}^{2}}{2 ρ v}$
Sound intensity level	$β (d B) = 10 {log}_{10} (\frac{I}{I_{0}})$
Resonant wavelengths of a tube closed at one end	$λ_{n} = \frac{4}{n} L, n = 1, 3, 5,…$
Resonant frequencies of a tube closed at one end	$f_{n} = n \frac{v}{4 L}, n = 1, 3, 5,…$
Resonant wavelengths of a tube open at both ends	$λ_{n} = \frac{2}{n} L, n = 1, 2, 3,…$
Resonant frequencies of a tube open at both ends	$f_{n} = n \frac{v}{2 L}, n = 1, 2, 3,…$
Beat frequency produced by two waves that differ in frequency	$f_{beat} = \| f_{2} - f_{1} \|$
Observed frequency for a stationary observer and a moving source	$f_{o} = f_{s} (\frac{v}{v \mp v_{s}})$
Observed frequency for a moving observer and a stationary source	$f_{o} = f_{s} (\frac{v \pm v_{o}}{v})$
Doppler shift for the observed frequency	$f_{o} = f_{s} (\frac{v \pm v_{o}}{v \mp v_{s}})$
Mach number	$M = \frac{v_{s}}{v}$
Sine of angle formed by shock wave	$sin θ = \frac{v}{v_{s}} = \frac{1}{M}$

Conceptual questions

What is the difference between a sonic boom and a shock wave?

Got questions? Get instant answers now!

Due to efficiency considerations related to its bow wake, the supersonic transport aircraft must maintain a cruising speed that is a constant ratio to the speed of sound (a constant Mach number). If the aircraft flies from warm air into colder air, should it increase or decrease its speed? Explain your answer.

The speed of sound decreases as the temperature decreases. The Mach number is equal to $M = \frac{v_{s}}{v},$ so the plane should slow down.

Got questions? Get instant answers now!

When you hear a sonic boom, you often cannot see the plane that made it. Why is that?

Got questions? Get instant answers now!

Problems

An airplane is flying at Mach 1.50 at an altitude of 7500.00 meters, where the speed of sound is $v = 343.00 m/s .$ How far away from a stationary observer will the plane be when the observer hears the sonic boom?

Got questions? Get instant answers now!

A jet flying at an altitude of 8.50 km has a speed of Mach 2.00, where the speed of sound is $v = 340.00 m/s .$ How long after the jet is directly overhead, will a stationary observer hear a sonic boom?

$\begin{matrix} θ = 30.02 ° \\ v_{s} = 680.00 m/s \\ tan θ = \frac{y}{v_{s} t}, t = 21.65 s \end{matrix}$

Got questions? Get instant answers now!

The shock wave off the front of a fighter jet has an angle of $θ = 70.00 °$ . The jet is flying at 1200 km/h. What is the speed of sound?

Got questions? Get instant answers now!

A plane is flying at Mach 1.2, and an observer on the ground hears the sonic boom 15.00 seconds after the plane is directly overhead. What is the altitude of the plane? Assume the speed of sound is $v_{w} = 343.00 m/s .$

$\begin{matrix} sin θ = \frac{1}{M}, θ = 56.47 ° \\ y = 9.31 km \end{matrix}$

Got questions? Get instant answers now!

<< Chapter < Page Page > Chapter >>

Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 1' conversation and receive update notifications?

Ask

	MAPEH Test G9 (Physical Education) By Angelica Lito Start Quiz
	NCE Ch 11 Counseling Families, Diagnosis... By Anh Dao Start Quiz
	2 Pharmacology Nervous System Essay By Rohini Ajay Start Test
	Spanish (Places) By Inderjeet Brar Start Flashcards
	13 Neuroanatomy 13 The Hypothalamus By Stephen Voron Start Quiz
	23 AP Key Terms 23 The Digestive System By OpenStax Start Key Terms
	15 Dr. Amberg Pharm quiz By Brooke Delaney Start Exam
	5 Microeconomics 05 Elasticity By OpenStax Start Flashcards
	21 AP 21 Lymphatic Immune System MCQ By OpenStax Start Quiz
	26 Toxicology Gustafson- Biotoxins and Venoms By Brooke Delaney Start Exam