17.8 Shock Waves

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.

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

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 $v_{\text{w}} = 343.00 \text{m}/\text{s} .$

A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency of f, creating a sound wave that moves down the tube. The wave moves through the tube at a speed of $v = 340.00 \text{m}/\text{s} .$ The sound wave is modeled with the wave function $s \left(x , t\right) = s_{\text{max}} \text{cos} \left(k x - \omega t + \phi\right)$. At time $t = 0.00 \text{s}$, an air molecule at $x = 2.3 \text{m}$ is at the maximum displacement of 6.34 nm. At the same time, another molecule at $x = 2.7 \text{m}$ has a displacement of 2.30 nm.…

A 0.80-m-long tube is opened at both ends. The air temperature is $26 ° \text{C} .$ The air in the tube is oscillated using a speaker attached to a signal generator. What are the wavelengths and frequencies of first two modes of sound waves that resonate in the tube?

Two cars move toward one another, both sounding their horns $\left(f_{s} = 800 \text{Hz}\right)$. Car A is moving at 65 mph and Car B is at 75 mph. What is the beat frequency heard by each driver? The air temperature is $T_{C} = 22.00 ° \text{C}$.

Suppose that the sound level from a source is 75 dB and then drops to 52 dB, with a frequency of 600 Hz. Determine the (a) initial and (b) final sound intensities and the (c) initial and (d) final sound wave amplitudes. The air temperature is $T_{\text{C}} = 24.00 ° \text{C}$ and the air density is $\rho = 1.184 \text{kg}/\text{m}^{3} .$

A stationary observer hears a frequency of 1000.00 Hz as a source approaches and a frequency of 850.00 Hz as a source departs. The source moves at a constant velocity of 75 mph. What is the temperature of the air?

Two sound speakers are separated by a distance d, each sounding a frequency f. An observer stands at one speaker and walks in a straight line a distance x, perpendicular to the the two speakers, until he comes to the first maximum intensity of sound. The speed of sound is v. How far is he from the speaker? Assume the distance, d, between the slits is larger than the wavelength of the sound.

A string $\left(\mu = 0.006 \frac{\text{kg}}{\text{m}} , L = 1.50 \text{m}\right)$ is fixed at both ends and is under a tension of 155 N. It oscillates in the $n = 10$ mode and produces sound. A tuning fork is ringing nearby, producing a beat frequency of 23.76 Hz. (a) What is the frequency of the sound from the string? (b) What is the frequency of the tuning fork if the tuning fork frequency is lower? (c) What should be the tension of the string for the beat frequency to be…

A string has a linear mass density $\mu = 0.007 \text{kg}/\text{m},$ a length $L = 0.70 \text{m},$ a tension of $F_{T} = 110 \text{N} ,$ and oscillates in a mode $n = 3$. (a) What is the frequency of the oscillations? (b) Use the result in the preceding problem to find the change in the frequency when the tension is increased by $1.00 \%$.

A string on the violin has a length of 23.00 cm and a mass of 0.900 grams. The tension in the string 850.00 N. The temperature in the room is $T_{C} = 24.00 ° \text{C} .$ The string is plucked and oscillates in the $n = 9$ mode. (a) What is the speed of the wave on the string? (b) What is the wavelength of the sounding wave produced? (c) What is the frequency of the oscillating string? (d) What is the frequency of the sound produ…