# 17.8 Shock waves  (Page 5/8)

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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 ${T}_{\text{C}}=24.00\text{°}\text{C}$ and the air density is $\rho =1.184\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}.$

$v=345.24\frac{\text{m}}{\text{s}}$ ; a. $I=31.62\frac{\text{μW}}{{\text{m}}^{2}}$ ; b. $I=0.16\frac{\text{μW}}{{\text{m}}^{2}}$ ; c. ${s}_{\text{max}}=104.39\phantom{\rule{0.2em}{0ex}}\text{μm}$ ; d. ${s}_{\text{max}}=7.43\phantom{\rule{0.2em}{0ex}}\text{μm}$

The Doppler shift for a Doppler radar is found by $f={f}_{R}\left(\frac{1+\frac{v}{c}}{1-\frac{v}{c}}\right)$ , where ${f}_{R}$ is the frequency of the radar, f is the frequency observed by the radar, c is the speed of light, and v is the speed of the target. What is the beat frequency observed at the radar, assuming the speed of the target is much slower than the speed of light?

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?

$\begin{array}{}\\ \\ \frac{{f}_{A}}{{f}_{D}}=\frac{v+{v}_{\text{s}}}{v-{v}_{\text{s}}},\phantom{\rule{0.5em}{0ex}}\left(v-{v}_{\text{s}}\right)\frac{{f}_{A}}{{f}_{D}}=v+{v}_{\text{s}},\phantom{\rule{0.5em}{0ex}}v=347.39\frac{\text{m}}{\text{s}}\hfill \\ {T}_{\text{C}}=27.70\text{°}\hfill \end{array}$

A flute plays a note with a frequency of 600 Hz. The flute can be modeled as a pipe open at both ends, where the flute player changes the length with his finger positions. What is the length of the tube if this is the fundamental frequency?

## Challenge problems

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?

$\begin{array}{}\\ \\ \sqrt{{x}^{2}+{d}^{2}}-x=\lambda ,\phantom{\rule{0.5em}{0ex}}{x}^{2}+{d}^{2}={\left(\lambda +x\right)}^{2}\hfill \\ \\ \\ {x}^{2}+{d}^{2}={\lambda }^{2}+2x\lambda +{x}^{2},\phantom{\rule{0.5em}{0ex}}{d}^{2}={\lambda }^{2}+2x\lambda \hfill \\ \\ \\ \\ \\ x=\frac{{d}^{2}-{\left(\frac{v}{f}\right)}^{2}}{2\frac{v}{f}}\hfill \end{array}$

Consider the beats shown below. This is a graph of the gauge pressure versus time for the position $x=0.00\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$ The wave moves with a speed of $v=343.00\phantom{\rule{0.2em}{0ex}}\text{m/s}\text{.}$ (a) How many beats are there per second? (b) How many times does the wave oscillate per second? (c) Write a wave function for the gauge pressure as a function of time. Two speakers producing the same frequency of sound are a distance of d apart. Consider an arc along a circle of radius R , centered at the midpoint of the speakers, as shown below. (a) At what angles will there be maxima? (b) At what angle will there be minima? a. For maxima $\begin{array}{}\\ \\ \text{Δ}r=d\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta \hfill \\ d\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta =n\lambda \phantom{\rule{0.5em}{0ex}}n=0,±1,±2\text{....},\phantom{\rule{0.5em}{0ex}}\theta ={\text{sin}}^{-1}\left(n\frac{\lambda }{d}\right)\phantom{\rule{0.5em}{0ex}}n=0,±1,±2\text{....}\hfill \end{array}$
b. For minima, $\begin{array}{}\\ \\ \text{Δ}r=d\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta \hfill \\ d\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta =\left(n+\frac{1}{2}\right)\lambda \phantom{\rule{0.5em}{0ex}}n=0,±1,±2\text{....}\hfill \\ \theta ={\text{sin}}^{-1}\left(\left(n+\frac{1}{2}\right)\frac{\lambda }{d}\right)\phantom{\rule{0.5em}{0ex}}n=0,±1,±2\text{....}\hfill \end{array}$

A string has a length of 1.5 m, a linear mass density $\mu =0.008\phantom{\rule{0.2em}{0ex}}\text{kg/m,}$ , and a tension of 120 N. If the air temperature is $T=22\text{°}\text{C,}$ what should the length of a pipe open at both ends for it to have the same frequency for the $n=3$ mode?

A string $\left(\mu =0.006\frac{\text{kg}}{\text{m}},L=1.50\phantom{\rule{0.2em}{0ex}}\text{m}\right)$ 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 zero?

a. ${v}_{\text{string}}=160.73\frac{\text{m}}{\text{s}},\phantom{\rule{0.5em}{0ex}}{f}_{\text{string}}=535.77\phantom{\rule{0.2em}{0ex}}\text{Hz}$ ; b. ${f}_{\text{fork}}=512\phantom{\rule{0.2em}{0ex}}\text{Hz}$ ; c. ${f}_{\text{fork}}=\frac{n\sqrt{\frac{{F}_{T}}{\mu }}}{2L},\phantom{\rule{0.5em}{0ex}}{F}_{T}=141.56\phantom{\rule{0.2em}{0ex}}\text{N}$

A string has a linear mass density $\mu$ , a length L , and a tension of ${F}_{T}$ , and oscillates in a mode n at a frequency f . Find the ratio of $\frac{\text{Δ}f}{f}$ for a small change in tension.

A string has a linear mass density $\mu =0.007\phantom{\rule{0.2em}{0ex}}\text{kg/m,}$ a length $L=0.70\phantom{\rule{0.2em}{0ex}}\text{m,}$ a tension of ${F}_{T}=110\phantom{\rule{0.2em}{0ex}}\text{N},$ 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 $1.00\text{%}$ .

a. $f=268.62\phantom{\rule{0.2em}{0ex}}\text{Hz}$ ; b. $\text{Δ}f\approx \frac{1}{2}\phantom{\rule{0.2em}{0ex}}\frac{\text{Δ}{F}_{T}}{{F}_{T}}f=1.34\phantom{\rule{0.2em}{0ex}}\text{Hz}$

A speaker powered by a signal generator is used to study resonance in a tube. The signal generator can be adjusted from a frequency of 1000 Hz to 1800 Hz. First, a 0.75-m-long tube, open at both ends, is studied. The temperature in the room is ${T}_{\text{F}}=85.00\text{°}\text{F}\text{.}$ (a) Which normal modes of the pipe can be studied? What are the frequencies and wavelengths? Next a cap is place on one end of the 0.75-meter-long pipe. (b) Which normal modes of the pipe can be studied? What are the frequencies and wavelengths?

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 ${T}_{C}=24.00\text{°}\text{C}\text{.}$ 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 produced? (e) What is the wavelength of the sound produced?

a. $v=466.07\frac{\text{m}}{\text{s}}$ ; b. ${\lambda }_{9}=51.11\phantom{\rule{0.2em}{0ex}}\text{mm}$ ; c. ${f}_{9}=9.12\phantom{\rule{0.2em}{0ex}}\text{kHz}$ ;
d. ${f}_{\text{sound}}=9.12\phantom{\rule{0.2em}{0ex}}\text{kHz}$ ; e. ${\lambda }_{\text{air}}=37.86\phantom{\rule{0.2em}{0ex}}\text{mm}$

#### Questions & Answers

definition of inertia
philip Reply
the reluctance of a body to start moving when it is at rest and to stop moving when it is in motion
charles
An inherent property by virtue of which the body remains in its pure state or initial state
Kushal
why current is not a vector quantity , whereas it have magnitude as well as direction.
Aniket Reply
why
daniel
the flow of current is not current
fitzgerald
bcoz it doesn't satisfy the algabric laws of vectors
Shiekh
The Electric current can be defined as the dot product of the current density and the differential cross-sectional area vector : ... So the electric current is a scalar quantity . Scalars are related to tensors by the fact that a scalar is a tensor of order or rank zero .
Kushal
what is binomial theorem
Tollum Reply
hello are you ready to ask aquestion?
Saadaq Reply
what is binary operations
Tollum
What is the formula to calculat parallel forces that acts in opposite direction?
Martan Reply
position, velocity and acceleration of vector
Manuel Reply
hi
peter
hi
daniel
hi
Vedisha
*a plane flies with a velocity of 1000km/hr in a direction North60degree east.find it effective velocity in the easterly and northerly direction.*
imam
hello
Lydia
hello Lydia.
Sackson
What is momentum
isijola
hello
Saadaq
A rail way truck of mass 2400kg is hung onto a stationary trunk on a level track and collides with it at 4.7m|s. After collision the two trunk move together with a common speed of 1.2m|s. Calculate the mass of the stationary trunk
Ekuri Reply
I need the solving for this question
philip
is the eye the same like the camera
EDWIN Reply
I can't understand
Suraia
same here please
Josh
I think the question is that ,,, the working principal of eye and camera same or not?
Sardar
yes i think is same as the camera
muhammad
what are the dimensions of surface tension
samsfavor
why is the "_" sign used for a wave to the right instead of to the left?
MUNGWA Reply
why classical mechanics is necessary for graduate students?
khyam Reply
classical mechanics?
Victor
principle of superposition?
Naveen Reply
principle of superposition allows us to find the electric field on a charge by finding the x and y components
Kidus
Two Masses,m and 2m,approach each along a path at right angles to each other .After collision,they stick together and move off at 2m/s at angle 37° to the original direction of the mass m. What where the initial speeds of the two particles
MB
2m & m initial velocity 1.8m/s & 4.8m/s respectively,apply conservation of linear momentum in two perpendicular directions.
Shubhrant
A body on circular orbit makes an angular displacement given by teta(t)=2(t)+5(t)+5.if time t is in seconds calculate the angular velocity at t=2s
MB
2+5+0=7sec differentiate above equation w.r.t time, as angular velocity is rate of change of angular displacement.
Shubhrant
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
Daniel Reply
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
Goodness Reply
(10/6) ÷0.4=4.167 per sec
Shubhrant
what is the formula for pressure?
Goodness Reply
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
John Reply
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
Daniel
and the color spectrum
Daniel

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