The angular frequency is 1650 rad/s, so x = (1.5 x 10-4m)cos (1650t). Note that the directional pattern is exactly the same for every speaker with the same \( L/\lambda \) ratio, such as an 12" (30cm) speaker at 2kHz, or a 48" speaker at 500Hz. PipeBhas a lengthL/2 and has one open end and one closed end. (b) Which substance inTable 17.1is this likely to be? The maximum acceleration is 410 m/s2, so a = - (410 m/s2)cos (1650t). (b) What is the wavelength of the sounding wave produced? The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. They can only convert 0 .5% to 2% of the power they consume into acoustic power. sinusoidal base excitation with an amplitude The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics. Why might this be? Solution a. The air around the string oscillates at the frequency of the string. What is the difference between a sonic boom and a shock wave? Show that the speed of sound in20.0C20.0Cair is343m/s,343m/s,as claimed in the text. (a) What do you think the frequency of the sound wave is that the vibrating string produces? What is the difference between sound and hearing? (a) At what angles will there be maxima? Science Physics Physics questions and answers 3 (a) A loudspeaker oscillates with frequency f to produce sound waves of wavelength 2. ), What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? Find:- . What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz? Shown are snapshots of the wave function fort=0.000st=0.000s(blue) andt=0.005st=0.005s(orange). Consider the graph shown below of a compression wave. The speaker oscillates at a frequency of f, creating a sound wave that moves down the tube. What beat frequencies are present: (a) If the musical notes A and C are played together (frequencies of 220 and 264 Hz)? Sound waves can be modeled as a change in pressure. The ambulance is moving at 70.00 mph. Calculate the speed of sound on a day when a 1500-Hz frequency has a wavelength of 0.221 m. (a) What is the speed of sound in a medium where a 100-kHz frequency produces a 5.96-cm wavelength? The sound wave is modeled with the wave function s(x,t)= smaxcos(kxt+) s ( x, t) = s max cos ( k x t + ). whereis the density of the medium in which the sound wave travels andvwvwis the speed of sound in the medium. Sound can be modeled in terms of pressure or in terms of displacement of molecules. (b) What are the velocity and acceleration as a function of time? A string has a length of 1.5 m, a linear mass density=0.008kg/m,=0.008kg/m,, and a tension of 120 N. If the air temperature isT=22C,T=22C,what should the length of a pipe open at both ends for it to have the same frequency for then=3n=3mode? Hence employing 220 nF capacitors provides an functioning frequency of around 100 Hz, and 2.2 nF capacitors would deliver oscillation at around 10 kHz. =mcos5.88rad/st+ . (1) Too low a voltage can result in a lack of regulation. What beat frequency do they produce? A person has a hearing threshold 10 dB above normal at 100 Hz and 50 dB above normal at 4000 Hz. a. What frequency does the nurse observe? A concept closely related to period is the frequency of an event. A 1024-Hz tuning fork is struck and the beat frequency between the two sources is 52.83 Hz. Take the speed of sound to be 331 m/s. A nurse is approaching the scene from the opposite direction, running atvo=7.00m/s.vo=7.00m/s. We have to calculate the acceleration in a B part. (a) What are the wavelength and the frequency of the fundamental frequency? An airplane is flying at Mach 1.50 at an altitude of 7500.00 meters, where the speed of sound isv=343.00m/s.v=343.00m/s. A:Given data: The ear canal resonates like a tube closed at one end. That is, what speed produces a shift of0.300%0.300%on a day when the speed of sound is 331 m/s? What is the maximum change in pressure, the wavelength, the frequency, and the speed of the sound wave? What is the minimum speed at which a source must travel toward you for you to be able to hear that its frequency is Doppler shifted? If the frequency of each speaker is doubled, what is the beat frequency produced? Check that 15 volts is correct. Ignoring the mass of the spring, what is the mass m of the fish? At time t=0.00 s , an air molecule at x=3.5 m is at the maximum displacement of 7.00 nm. Frequency = 1 / period. You should learn how to use LaTex. With the help of the frequency,, Q:A block-spring system has a maximum restoring force Fmax 0.1 N. If the Is the frequency the same for both tubes? The air temperature isTC=24.00CTC=24.00Cand the air density is=1.184kg/m3.=1.184kg/m3. The perception of intensity is loudness and loudness has units of phons. Consider the sound created by resonating the tube shown below. v = 340.00 m/s. What is the flatcars speed in mph? When you hear a sonic boom, you often cannot see the plane that made it. (a) If a submarines sonar can measure echo times with a precision of 0.0100 s, what is the smallest difference in distances it can detect? The total mass of the block and speaker is 5.00 kg, and the amplitude of this unit's motion is 0.500 m. (a) If the speaker emits sound waves of frequency 440 Hz, determine the highest and lowest frequencies heard by the person to . A:The angle of simple pendulum is given by, Consider an arc along a circle of radiusR, centered at the midpoint of the speakers, as shown below. .076 m A 160 g air-track glider is attached to a spring. Yes, the frequency of the sound played by the speaker is exactly the frequency of the current that flows through the coil (electromagnet). By what fraction will the frequencies produced by a wind instrument change when air temperature goes from10.0C10.0Cto30.0C30.0C? The speed of sound in the steel beam isv=5950m/s.v=5950m/s. What is the speed of the ambulance (in mph) if the speed of sound isv=340.00m/s?v=340.00m/s? The cone of a loudspeaker oscillates in SHM at a frequency of 262 Hz. If the frequency is 2.5 kHz, what are the maximum velocity and the maximum acceleration of the cone? Student A carries a tuning fork ringing at 1024 Hz, and student B carries a tuning fork ringing at 1000 Hz. This crossword clue Low-frequency loudspeaker was discovered last seen in the February 5 2021 at the NewsDay Crossword. (14-10) A mass m at the end of a spring oscillates with a frequency of 0.83 Hz. If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect? The wave moves with a speed ofv=343.00m/s.v=343.00m/s. Find the wave function for the sound wave in the steel beam. 1.7 Hz 12. This is why loudspeakers are technically called drivers: they "drive" (move) the air to produce sound. (See [link]Figure 17_03_HumEar[/link].) The sound wave is modeled with the wave function s(x,t)= smaxcos(kxt+). If a woman needs an amplification of5.01055.0105times the threshold intensity to enable her to hear at all frequencies, what is her overall hearing loss in dB? The length of a pincil is measured to be 14.65cm.what is the values in one significant figure; 4. That is called a simple motion. An organ pipe(L=3.00m)(L=3.00m)is closed at one end. (a) Which normal modes of the pipe can be studied? The 1.1 kg mass is removed and replaced with a 1.4 kg mass. Next a cap is place on one end of the 0.75-meter-long pipe. What is the principle used in this device? The wave moves through the tube at a speed of v = 340.00 m/s. The tension in the string and the linear mass density is such that the speed of a wave on the string isv=343m/s.v=343m/s. velocity and acceleration as a function of time? motion of the center of the cone? The jet is flying at 1200 km/h. 12 kg is attached to (a) What equation describes the motion of the center of the cone? Science Physics The cone of a loudspeaker oscillates in SHM at a frequency of 262 Hz ("middle C"). The transducer is to be used in nondestructive testing to test for fractures in steel beams. Find the amplitude and phase constant for the motion. When a frequency of 60 Hz is applied, the string vibrates in the standing wave pattern shown. The displacement of the air molecules in sound wave is modeled with the wave functions(x,t)=5.00nmcos(91.54m1x3.14104s1t)s(x,t)=5.00nmcos(91.54m1x3.14104s1t). An airplane moves at Mach 1.2 and produces a shock wave. Consider the graph in the preceding problem of a compression wave. (b) What are the period and wavelength of the sound wave? Basically, we obtain a huge increase in the amplitude of oscillations as we tune the natural frequency \omega_0 0 close to the driving frequency \omega . Frequency f is defined to be the number of events per unit time. 3. 4. For periodic motion, frequency is the number of oscillations per unit time. Why is the change in pressure used and not the actual pressure? How much more intense must a 100-Hz tone be than a 4000-Hz tone if they are both barely audible to this person? Sound has the same properties of interference and resonance as defined for all waves. Rutgers, The State University of New Jersey. Two loudspeakers, S1 and S2, each emit a musical note of frequency 2.5 kHz with identical signal amplitude. Two identical strings, of identical lengths of 2.00 m and linear mass density of=0.0065kg/m,=0.0065kg/m,are fixed on both ends. 13 points 18 joules per second is what we get after multiplication. Ten cars in a circle at a boom box competition produce a 120-dB sound intensity level at the center of the circle. 3 (a) A loudspeaker oscillates with frequency f to produce sound waves of wavelength 2. The string is plucked and oscillates in then=9n=9mode. A person's mass is 72.8 kg. (c) What is the position of the cone at t = 1.00 ms (= 1.00 x 10-3 s)? (b)a=3, b=4 and, Q:The period of oscillation of a spring-and-mass system is 0.600 s and the amplitude is 4.97 cm. The speaker oscillates at a frequency off, creating a sound wave that moves down the tube. What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? A sonar echo returns to a submarine 1.20 s after being emitted. We get 21.98 into 10 days. Assume the speed of sound isv=343.00m/s.v=343.00m/s. Her mass is 55.0 kg and the period of her motion is, A:Mass of the female diver(m1)=55kg What is the total distance the particle travels in one period? The cone of a loud speaker oscillates in simple harmonic motion at a frequency of 262 Hz ("middle C*). 4A 10. Take air temperature to be37.0C,37.0C,which is the same as body temperature. At t = 0, the object is at x = 4.0 cm with an initial velocity vx = -25cm/s a. Two speakers producing the same frequency of sound are a distance ofdapart. Unwanted sound can be reduced using destructive interference. Please upload the remaining part of, Q:When the displacement in SHM is one-half the amplitude xm what fraction of the total energy is, Q:A mass m Put the values of all these terms into 10 days and you'll get 0.4 In 221.98, 1.5 In 2, and 3 in 10 days to park. The cone of a loudspeaker oscillates in SHM at a frequency of 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. The cone of a loudspeaker oscillates with simple harmonic motion: It vibrates with frequency of 3.5 kHz and an amplitude of 5 mm It takes the soundt=0.10st=0.10sto reach the meter. (a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? (b) What are the frequency and wavelength of the first overtone? What i. The density of a sample of water is=998.00kg/m3=998.00kg/m3and the bulk modulus is=2.15GPa.=2.15GPa. the center, A:SOlution: (Assume that the submarine is in the ocean, not in fresh water.) How does an unamplified guitar produce sounds so much more intense than those of a plucked string held taut by a simple stick? For a series b. What is the maximum displacement, the wavelength, the frequency, and the speed of the sound wave? a dB meter registered 130 dB when placed 2.7 m in front of a loudspeaker on the stage. perception of the frequency of a sound shock wave wave front that is produced when a sound source moves faster than the speed of sound sonic boom loud noise that occurs as a shock wave as it sweeps along the ground sound traveling pressure wave that may be periodic; the wave can be modeled as a pressure wave or as an oscillation of molecules Two sound speakers are separated by a distanced, each sounding a frequencyf. An observer stands at one speaker and walks in a straight line a distancex, perpendicular to the the two speakers, until he comes to the first maximum intensity of sound. Suppose that the sound level from a source is 75 dB and then drops to 52 dB, with a frequency of 600 Hz. The air temperature isTC=22.00CTC=22.00C. A community is concerned about a plan to bring train service to their downtown from the towns outskirts. The time period of a simple pendulum is defined as the time taken by the pendulum to finish one complete oscillation. The second observer notes the difference as 3.00 seconds. The value of velocity can be written as we go into a motion. s(x,t)=4.50nmcos(9.15104m1x2(5.00MHz)t). This is often caused by a feeble battery whose internal resistance is too high, allowing the DC supply voltage to vary. It will take 1.5 into 10 days to park. What will the frequency be if the inductance is quadrupled? The amplitude of a sound wave is measured in terms of its maximum gauge pressure. At timet=0.00st=0.00s, an air molecule atx=2.3mx=2.3mis at the maximum displacement of 6.34 nm. Calculate the first overtone in an ear canal, which resonates like a 2.40-cm-long tube closed at one end, by taking air temperature to be37.0C37.0C. unit of frequency is hertz,denoted by Hz. If the aircraft flies from warm air into colder air, should it increase or decrease its speed? He strikes the fork and hits a key on the piano and hears a beat frequency of 5 Hz. Could you give me any equations, with explanations? (a) What is the fundamental frequency if the tube is 0.240 m long, by taking air temperature to be37.0C37.0C? What are the possible frequency and wavelength of the wave on the string? The source moves at a constant velocity of 75 mph. time? simple harmonic motion is given by x- Ssin Answers and Replies Jun 1, 2010 #2 ehild Homework Helper The Doppler shift for a Doppler radar is found byf=fR(1+vc1vc)f=fR(1+vc1vc), wherefRfRis the frequency of the radar,fis the frequency observed by the radar,cis the speed of light, andvis the speed of the target. (b) What percent uncertainty does this cause for the bat in locating the insect? The speed of sound isv=343.00m/s.v=343.00m/s. In air, the speed of sound is related to air temperature, Sound intensity level in units of decibels (dB) is. You will learn that light is an electromagnetic wave that can travel through a vacuum. It may not display this or other websites correctly. f1=1000Hz. What equation describes the motion of the center of the cone? The maximum velocity is 0.25 m/s, so v = - (0.25 m/s)sin (1650t). Ultrasonic sound waves are often used in methods of nondestructive testing. One day, they were asked to leave the pool so the dive team could practice a few dives, and they tried to practice on a mat, but seemed to have a lot more difficulty. 5.2. (b) What are the velocity and acceleration as a function of time? In air columns, the lowest-frequency resonance is called the fundamental, whereas all higher resonant frequencies are called overtones. The air temperature of the night air isTF=90.00F.TF=90.00F. The less damping a system has, the higher the amplitude of the forced oscillations near resonance. Compute the wavelengths and frequencies of the first three modes of resonance. A .75-kg toy oscillating on a spring completes a cycle every 0.60 s. What is the frequency of this oscillation? Calcu; 2. A sound wave is modeled with the wave functionP=1.20Pasin(kx6.28104s1t)P=1.20Pasin(kx6.28104s1t)and the sound wave travels in air at a speed ofv=343.00m/s.v=343.00m/s. Exact plots require that a vertical asymptote at fn be approached on each side by a curve tending to . f = 2.0 Hz. (a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is18.0C18.0C. Should the townspeople be concerned? The signal generator can be adjusted from a frequency of 1000 Hz to 1800 Hz. When I typed Loudspeaker equations into google I got this. I think I understand first two equations well, but please correct me if I am wrong: m - mass of the coil and the piece of iron??? The air in the tube is oscillated using a speaker attached to a signal generator. A system's natural frequency is the frequency at which the system oscillates if not affected by driving or damping forces. The value of power loss should be close to force. ExAMPLE 14.1 physicsfor instance, the object Frequency and period of a loudspeaker cone What is the oscillation period of a loudspeaker cone that vibrates back and forth 5000 times per second? Magnitude of acceleration when displacement is maximum. What beat frequencies are produced by this discordant combination? We learnt that v = f , where v is the speed of the wave, f is the frequency of the wave and is the wavelength of the wave. In this problem, f = 2.0 Hz. (b) If the speed of sound in tissue is 1800 m/s, what is the wavelength of this wave in tissue? What is the length of the tube? Sometimes, a LM386 will oscillate at lower audio frequencies when a heavy load like a speaker is inserted. First, a 0.75-m-long tube, open at both ends, is studied. s(x,t)=6.00nmcos(54.93m1x18.84103s1t). B. c. At t = 1 ms, x = -1.2 x 10-5m. a) What equation describes the motion of the center of the The amplitude at the center of the cone is A = 1.5 x 10-4 m, and at t = 0, x = A. Collectively, they are called harmonics. Can you perceive the shift in frequency produced when you pull a tuning fork toward you at 10.0 m/s on a day when the speed of sound is 344 m/s? How to derive Nielsen equation from Lagrange equation? What average frequency will you hear, and what will the beat frequency be? It is reasonable to assume that sound is transmitted into a stethoscope 100 times as effectively compared with transmission though the air. What are the frequencies and wavelengths? Is the ear particularly sensitive to such a frequency? How long after the jet is directly overhead, will a stationary observer hear a sonic boom? At timet=0.00st=0.00s, an air molecule atx=3.5mx=3.5mis at the maximum displacement of 7.00 nm. The next resonance is reached when the piston is 82.50 cm from the open end. As the water is emptied from the tube, the lengthLof the air column changes. A speaker powered by a signal generator is used to study resonance in a tube. A body vibrating with simple harmonic motion has a frequency of 4Hz and an amplitude of 0.15m. In conclusion. The accuracy of it's response determines the quality. Two tuning forks having frequencies of 460 and 464 Hz are struck simultaneously. What is the beat frequency heard by each driver? The crossword clue possible answer is available in 6 letters. What is its wavelength if the speed of sound is 345 m/s? Generally, the equation for the Freqency is mathematically given as. A string has a linear mass density=0.007kg/m,=0.007kg/m,a lengthL=0.70m,L=0.70m,a tension ofFT=110N,FT=110N,and oscillates in a moden=3n=3. What is the frequency f of the first possible harmonic after the fundamental . Why do you suppose the room temperature is required? A 1024-Hz tuning fork is placed at the opening of the tube. (b) What is the value forP(3.00m,20.00s)P(3.00m,20.00s)? The sound wave is modeled with the wave function s (x, t) = s_ {max} cos (kx - t + ). To answer this question, calculate the factor by which the frequency shifts and see if it is greater than 0.300%. What are the closest frequencies to 500 Hz that an average person can clearly distinguish as being different in frequency from 500 Hz? Assume the speed of sound to be the same in both tubes. If the frequency is $2.5 \mathrm{kHz}$. (The overtones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end.). So the angular frequency is (d) 0.419 rad The angle (with respect to the vertical) of a simple pendulum is given by e. The temperature in the room isTF=85.00F.TF=85.00F. A:Write the given equation and substitute 0 s for t and 0.035 rad for . Q:The position of an object undergoing SHM is given byx(t) = 2.5 cos t,withxin meters andtin, Q:What is the maximum acceleration of a platform that oscillates at amplitude 2.20 cm and frequency, Q:The acceleration of an oscillator undergoing simple harmonic motion is described by the equation, A:The oscillators position can be represented as, If the sound waves travel through air at a speed ofv=343m/s,v=343m/s,what is the wavelength of the sound waves? Loudspeaker designers therefore search for cone materials that combine high stiffness with low mass. What is the value of m? a spring with negligible mass and At t = 0, the object is at x = 4.0 cm with an initial . The flute can be modeled as a pipe open at both ends, where the flute player changes the length with his finger positions. The cone of a loudspeaker oscillates in SHM at a frequency of 262 Hz (middle C). (a) What is the wavelength and the frequency of the fundamental frequency? (In practice, the bat continues to use sound as it closes in, eliminating most of any difficulties imposed by this and other effects, such as motion of the prey.). Calculate the power input needed to produce a 90.0-dB sound intensity level for a 12.0-cm-diameter speaker that has an efficiency of1.00%1.00%. A loudspeaker oscillates with frequency f to produce sound waves of wavelength . Numerade The piston is slid down the pipe and resonance is reached when the piston is 115.50 cm from the open end. During a 4th of July celebration, an M80 firework explodes on the ground, producing a bright flash and a loud bang. (a) What is the fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s? (c) If all four are played together? (i) Define electromotive force (emf). The loudness of the speaker depends primarily on the intensity of the current through the coil ( http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html#c2") and the strength of the permanent magnet. (Assume the phase shift is zero.) (a) What is the wave number of the sound wave? Median response time is 34 minutes for paid subscribers and may be longer for promotional offers. A crude approximation of voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end. What happened? The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer. In which of the tubes could the highest fundamental frequency be produced? Assume the speed of sound isvw=343.00m/s.vw=343.00m/s. I think of a speaker as a servo device. K2 = 3K1. The wave moves through the tube at a speed of v=340.00 m/s. A sound wave of a frequency of 2.00 kHz is produced by a string oscillating in then=6n=6mode. NOTE: The S.I. Question Parameter(s): An lc circuit oscillates at a frequency of 2000 Hz. 0 = 8.85 1012 F m 1 (1 4 . the ratio of, Q:A 0.400 kg object undergoing SHM has ax = -1.80 m/s2 when x = 0.300 m. What is the time for one, A:Given: mass, M = 0.400kg, If a particle in simple harmonic motion has a maximum speed vmax= 0.2n m/s, A:The maximum speed of the particle is given as, Both screech, the first one emitting a frequency of 3200 Hz and the second one emitting a frequency of 3800 Hz. Is it ok to use approximation for long solenoid here, B= 0nI? What are the wavelength, wave speed, and frequency of the sound produced? A speaker capable of producing variable frequencies is placed at the open end and is used to cause the tube to resonate. Thermal Expansion in Two and Three Dimensions, Vapor Pressure, Partial Pressure, and Daltons Law, Heat Capacity of an Ideal Monatomic Gas at Constant Volume, Chapter 3 The First Law of Thermodynamics, Quasi-static and Non-quasi-static Processes, Chapter 4 The Second Law of Thermodynamics, Creative Commons Attribution 4.0 International License, [latex]\Delta P=\Delta {P}_{\text{max}}\text{sin}(kx\mp \omega t+\varphi )[/latex], Displacement of the oscillating molecules of a, [latex]s(x,t)={s}_{\text{max}}\text{cos}(kx\mp \omega t+\varphi )[/latex], [latex]v=\sqrt{\frac{\beta }{\rho }}[/latex], [latex]v=\sqrt{\frac{\gamma RT}{M}}[/latex], Speed of sound in air as a function of temperature, [latex]v=331\frac{\text{m}}{\text{s}}\sqrt{\frac{{T}_{\text{K}}}{273\,\text{K}}}=331\frac{\text{m}}{\text{s}}\sqrt{1+\frac{{T}_{\text{C}}}{273^\circ\text{C}}}[/latex], Decrease in intensity as a spherical wave expands, [latex]{I}_{2}={I}_{1}{(\frac{{r}_{1}}{{r}_{2}})}^{2}[/latex], [latex]I=\frac{{(\Delta {p}_{\text{max}})}^{2}}{2\rho v}[/latex], [latex]\beta (dB)=10\,{\text{log}}_{10}(\frac{I}{{I}_{0}})[/latex], Resonant wavelengths of a tube closed at one end, [latex]{\lambda }_{n}=\frac{4}{n}L,n=1,3,5\text{,}[/latex], Resonant frequencies of a tube closed at one end, [latex]{f}_{n}=n\frac{v}{4L},n=1,3,5\text{,}[/latex], Resonant wavelengths of a tube open at both ends, [latex]{\lambda }_{n}=\frac{2}{n}L,n=1,2,3\text{,}[/latex], Resonant frequencies of a tube open at both ends, [latex]{f}_{n}=n\frac{v}{2L},n=1,2,3\text{,}[/latex], Beat frequency produced by two waves that, [latex]{f}_{\text{beat}}=|{f}_{2}-{f}_{1}|[/latex], Observed frequency for a stationary observer, [latex]{f}_{\text{o}}={f}_{\text{s}}(\frac{v}{v\mp {v}_{\text{s}}})[/latex], [latex]{f}_{\text{o}}={f}_{\text{s}}(\frac{v\pm{v}_{\text{o}}}{v})[/latex], [latex]{f}_{\text{o}}={f}_{\text{s}}(\frac{v\pm{v}_{\text{o}}}{v\mp {v}_{\text{s}}})[/latex], [latex]\text{sin}\,\theta =\frac{v}{{v}_{s}}=\frac{1}{M}[/latex]. The speaker oscillates at a frequency f, creating a sound wave that moves down the tube. Loudspeakers can produce intense sounds with surprisingly small energy input in spite of their low efficiencies. Three stationary observers observe the Doppler shift from a source moving at a constant velocity. If you could measure distances over the same range with a single instrument and the smallest distance you could measure was 1 mm, what would the largest be?
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