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physics
particle physics

Questions and Answers of Particle Physics

Two oboe players are next to each other on the stage. One is playing a \(350-\mathrm{Hz}\) note, and the other is playing a \(355-\mathrm{Hz}\) note. What is the beat frequency heard by the audience?
Two tuba players in a marching band appear to your trained ear to be playing the correct note, \(196 \mathrm{~Hz}\), but there is an annoying warble that you interpret as being four beats per second.
The lowest frequency a certain sound receiver can detect is \(760 \mathrm{~Hz}\). If the receiver detects a frequency of \(762 \mathrm{~Hz}\). that is then mixed with an unknown frequency, also
You have four electronic audio generators, A, B, C, and D, all producing tones near \(1200 \mathrm{~Hz}\) that are easily audible but not distinguishable by ear. When you increase the frequency of
One tuning fork vibrates at a frequency of \(528 \mathrm{~Hz}\), and a second one vibrates at \(524 \mathrm{~Hz}\), but you don't know which is which. After applying a small piece of modeling clay to
Three tenors are giving a concert at an outdoor amphitheater. What are the possible beat frequencies if tenor 1 holds a \(262-\mathrm{Hz}\) note while tenor 2 holds a \(264.3-\mathrm{Hz}\) note and
When two frequencies are added together, the beat frequency and the average frequency are an octave apart. What is the ratio of the original frequencies?
Two violin strings, each having a linear mass density of \(0.0014 \mathrm{~kg} / \mathrm{m}\) and under the same \(100-\mathrm{N}\) tension, have the same fundamental frequency of \(660
During a fire drill in your dormitory, you notice that the sound waves from the two alarms on your floor interfere with each other; you hear five beats every two seconds. (a) If the average of the
What happens to the magnitude of the Doppler shift you hear in the whistle of a passing train if you increase the distance between you and the tracks?
While driving down the road, you spot a friend standing on the sidewalk. You honk your horn at him while driving \(70 \mathrm{~km} / \mathrm{h}\). Your horn emits a frequency of \(360 \mathrm{~Hz}\).
The electric bells at your school buzz with a frequency of \(400 \mathrm{~Hz}\). If you are late for class and riding your bike down a hill toward the school at a constant speed of \(4.47 \mathrm{~m}
At the racetrack, you estimate that the whine of the cars changes by one octave as the cars pass. About how fast are the cars going?
How fast do you have to travel away from a stationary sound source in order for the frequency to be shifted by (a) \(1 \%,(b) 10 \%\), and (c) a factor of 2 ?
While you watch a parade, a band on a float passes you. You detect the frequency of a note played on a flute to be \(352 \mathrm{~Hz}\) when the float is coming toward you and \(347 \mathrm{~Hz}\)
You and a friend are riding bikes, you moving at \(9.72 \mathrm{~km} / \mathrm{h}\) and she moving at \(7.20 \mathrm{~km} / \mathrm{h}\). She is behind you and turns on her electric horn, which has a
While you are driving on a straight road at \(97 \mathrm{~km} / \mathrm{h}\), a police car traveling in the opposite direction comes toward you with the siren blaring, and the frequency you hear is
A car traveling west at \(90 \mathrm{~km} / \mathrm{h}\) along a road running parallel to a railroad track approaches a train traveling east at \(65 \mathrm{~km} / \mathrm{h}\). If the train's
A foghorn that emits a frequency of \(150 \mathrm{~Hz}\) is mounted on a buoy in the bay. If a ship approaches the buoy at \(21.2 \mathrm{~km} / \mathrm{h},\)(a) what frequency does the captain of
Two airplanes simulating a dogfight are headed right for each other, plane A moving at \(285 \mathrm{~km} / \mathrm{h}\) and plane B moving at \(295 \mathrm{~km} / \mathrm{h}\). The electronic
You stand in your yard and hold a battery-powered buzzer that is emitting a frequency of \(560 \mathrm{~Hz}\) as a friend stands next to you. (a) What frequency does your friend hear if you throw the
A dog whistle has a frequency of \(21 \mathrm{kHz}\), which is above the high end of the audible range for humans. At what minimum speed and in what direction must you travel in order to just hear
During trials of a new submarine, its speed is measured with an underwater sonar gun anchored to the ocean floor. The gun emits sound waves at a frequency \(f\), and these waves reflect off the
A device that both emits and receives sound waves is traveling at \(80 \mathrm{~km} / \mathrm{h}\). The emitted waves have a frequency of \(700 \mathrm{~Hz}\). If the waves are reflected off a
Two students standing \(54.9 \mathrm{~m}\) apart are tossing around footballs designed to whistle while they are airborne. (a) When student A throws her football toward student B at \(16.0
A supersonic jet airplane flying horizontally and passing directly overhead creates a shock wave that makes an angle of \(47^{\circ}\) with the horizontal. What is the speed of the airplane?
As a boat travels at \(48.0 \mathrm{~km} / \mathrm{h}\) across the surface of a still lake, the waves it creates in the water have a speed of \(20.1 \mathrm{~km} / \mathrm{h}\). What is the angle of
A speedboat traveling at \(73.0 \mathrm{~km} / \mathrm{h}\) causes a shock wave that makes an angle of \(14.3^{\circ}\) with the path of the boat. At what speed are the waves moving through the water?
Two jets flying at the same altitude pass over your head simultancously, one traveling at Mach 1. 5 and the other at Mach 2. 5. Which plane's sonic boom do you hear first?
While attending an air show, you observe a fighter jet traveling horizontally at a speed of Mach 1. 30. At the instant you hear the sonic boom, what is the angle between your line of sight to the jet
Many years ago, test pilots accelerating through Mach 1 reported that the ride was pretty rough just before Mach 1 but smoothed out suddenly as Mach 1 was breached. How can you account for this?
Concerned about being disturbed by sonic booms, residents near an Air Force base located along a seacoast submit a petition asking that all jet aircraft from the base head out to sea before attaining
A woman standing on the ground observes a jet directly overhead flying at an altitude of \(20,000 \mathrm{~m}\). If the jet has a speed of Mach 2 and its shock wave makes an angle of \(30^{\circ}\)
At a pistol range, a microphone is placed between a shooter and the target so that when a bullet is fired we can hear its sonic boom. A bullet passes by the microphone at a speed of Mach 2. 1. The
A jet flying directly over you at an altitude of \(3000 \mathrm{~m}\) produces a shock wave. If the angle of the shock wave is \(42^{\circ}\).(a) how long will it be until the sonic boom reaches you,
At White Sands, New Mexico, a car powered by a rocket engine passes you while you are standing still. If you hear the sonic boom \(0.045 \mathrm{~s}\) after the car passes and the angle of the shock
What does an observer hear on the ground before and after a sonic boom caused by a jet passing overhead?
Is a second sonic boom generated when a plane reaches a speed of Mach 2?
Two test pilots are flying in a jet trainer going faster than Mach 1. Can the pilot in the front of the cockpit hear the pilot in back?
Two guitar strings, 1 and 2 , plucked simultaneously produce standing waves described by\[\begin{aligned}& D_{1}=A \sin (a x) \cos (b t) \\& D_{2}=A \sin (q x) \cos (d t),\end{aligned}\]with \(a=14.5
A race car traveling at \(350 \mathrm{~km} / \mathrm{h}\) passes a spectator in the stands. If the spectator has an air horn that emits a sound of frequency \(400 \mathrm{~Hz}\), what is the range of
Which type of conic section (circle, ellipse, parabola, or hyperbola) is formed by the nodal-line pattern produced by two coherent sources of two-dimensional waves?(For a given nodal line, the
Why is the high-frequency "tweeter" on a stereo speaker usually much smaller than the low-frequency "woofer"?
You are standing beneath a Ferris wheel when two children riding in cars on opposite sides of the wheel both scream at \(600 \mathrm{~Hz}\). Your well-trained ears notice a beat frequency that is
You have tickets for an outdoor rock concert, fourth row from the stage. However, at that distance the intensity level is \(100 \mathrm{~dB}\), too loud to be enjoyable. You decide to move to a row
You want to build a portable device that can detect pirate radio stations broadcasting at about \(50 \mathrm{~W}\) of power a few miles from your beachfront home. You have a \(0.60-\mathrm{m}\)
Your car is third in line at a railroad crossing as a train moving at a constant speed approaches, with its whistle blowing constantly. To keep yourself from going crazy with the noise, you begin
Given the wave function for \(t=0.50 \mathrm{~s}\) shown in Figure 16. 25, draw the displacement curves of particles at \(x=0\) and \(x=1.0 \mathrm{~m}\) as the wave passes them. If the leading edge
Given the displacement curve shown in Figure 16. 26 for a bead at \(x=0\) on a string as a wave moving toward the right with a speed of \(2.0 \mathrm{~m} / \mathrm{s}\) passes, draw the wave function
The two pulses shown in Figure 16. 27 are traveling in opposite directions; both have a speed of \(1.0 \mathrm{~m} / \mathrm{s}\). Draw the sum of the two pulses at \(t=1.0 \mathrm{~s}, t=2.0
Consider a triangular wave pulse approaching the fixed end of a string (Figure 16.18). Sketch the shape of the string(a) when a point halfway up the leading edge of the pulse has reached the fixed
Let the triangular wave pulse of Figure 16.18 approach the free end of a string. Sketch the shape of the string(a) when a point halfway up the leading edge of the incident pulse has reached the fixed
(a) Consider the time-dependent wave function \[D_{y}=f(x, t)= \begin{cases}b(x-c t) & \text { for } 01.0 \mathrm{~m},\end{cases}\]where \(b=0.80\) and \(c=2.0 \mathrm{~m} / \mathrm{s}\). Plot the
You use a hammer to give a sharp horizontal blow to a \(10-\mathrm{kg}\) lead brick suspended from the ceiling by a wire that is \(5.0 \mathrm{~m}\) long. It takes \(70 \mathrm{~ms}\) for the pulse
A wire with linear mass density \(\mu=0.0500 \mathrm{~kg} / \mathrm{m}\) is held taut with a tension of 100 N. At what rate must energy be supplied to the wire to generate a traveling harmonic wave
Show that a sinusoidal traveling wave of the form \(f(x, t)=A \sin (k x-\omega t)\) satisfies the wave equation for any value of \(k\) and \(\omega\).
Is it possible for the same medium to carry both a longitudinal and a transverse wave? If so, give an example. If not, explain why not.
Suppose you have a light spring stretched out and one end is attached to a wall. With this setup, you can move the free end in any of three directions \((x, y, z)\). If the spring lies along, say,
Figure P16.3 is a snapshot at \(t=0.80 \mathrm{~s}\) of a wave pulse traveling on a string. Construct \((a)\) the wave function at \(t=1.1 \mathrm{~s}\) and \((b)\) the displacement curve for the
The graphs in Figure P16.4 show the displacement caused by a wave moving along a string at two instants, (a) \(t_{1}\) and (b) \(t_{2}\). Let \(v_{\mathrm{av}}\) denote the average speed of a piece
Figure P16.5 shows the displacement curve for the particle located at \(x=a\) as a wave moves to the right along a string. If the wave advances a distance \(a\) each second, draw the wave function at
Identical ropes were tied to two trees, and two men, A and \(B\), started shaking the free ends at the same instant a short while ago (Figure P16.6). Which rope has the greater tension? Which man is
What is the definition of frequency for a nonharmonic periodic wave?
You and a friend each have one rope. You tie the two ropes together and stand as far apart as possible, each holding one end of the new longer rope and pulling to put it under tension. You then begin
You are watching a ship being loaded with large crates. The ship is held in place by several long steel cables attached to the dock. At one point, a crate bumps one of the cables and sends a wave
A harmonic wave is made to travel along a string when you move your hand up and down. The wave has a specific period \(T_{1}\), wavelength \(\lambda_{1}\), amplitude \(A_{1}\), and speed \(c_{1}\),
Water parks often have a pool with a wave-making machine at one end, consisting of a piston that pushes water back and forth. There are some places in the pool where the waves make inner-tube riders
Suppose wave pulses in an aquarium are produced by a mechanical motor that moves a bob up and down at the surface. If the setup uses a \(10-\mathrm{W}\) motor and has a period of \(1.5 \mathrm{~s}\)
Figure P16.13 shows two waves in a rope approaching each other at instant \(t=0\). For any instant after \(t=0\), determine the maximum displacement that occurs \((a)\) at \(x=0,(b)\) at \(x=0.90
The two wave pulses in Figure P16.14 are traveling on the same string at \(t=1.0 \mathrm{~s}\). Sketch the shape of the string at this instant.Data from P16.14 D, (mm) pulse A 3.0 0 3.0 1.0 2.0 3.0
Suppose two waves, identical except for the direction of travel, approach each other in a medium that obeys Hooke's law. At certain instants, the waves interfere constructively at all positions. At
A harmonic wave traveling along a light string approaches a splice to a heavier string, as shown in Figure P16.16. Which changes as the wave crosses the boundary: wavelength, frequency, both, or
A transverse wave in a swimming pool reaches the concrete side and is reflected. Determine whether the reflected wave is inverted.
A rope is attached to a tree trunk and made taut, and then a pulse traveling rightward is sent along the rope. For each case depicted in Figure P16.18, determine whether or not the reflected pulse is
Figure P16.19 shows two strings of different linear mass densities, connected and held taut, at some instant. At some earlier instant, only one pulse existed on one of the strings. (a) Determine
You shake the end of a taut string, creating two periods of a traveling sinusoidal wave, as shown in Figure P16.20. The string you are shaking (string 1) is connected to a second, much more massive,
Figure P16.21 shows a pulse as it approaches a fixed end of a rope. Draw the shape of the rope halfway through the reflection (that is, when half of the pulse length is still moving to the right and
Walking along the beach, you notice that a new wave reaches the shore every \(4.0 \mathrm{~s}\), and you estimate the wave crests to be \(2.5 \mathrm{~m}\) apart. At what wave speed \(c\) are the
While on a sailboat at anchor, you notice that 12 waves pass its bow every minute. If the waves have a speed of \(6.0 \mathrm{~m} / \mathrm{s}\), what is the distance between two adjacent wave crests?
Participating in a human rally wave at a football game, you have to stand up every \(15 \mathrm{~s}\). (a) What is the wave frequency? (b) If the stadium is oval and the inner circumference of the
(a) Plot the time-independent wave function for the traveling pulse described by the time-dependent wave function\[D_{y}(x, t)=\frac{a}{b^{2}+(x-a)^{2}}\]with \(a=5.0 \mathrm{~m}^{3}, b=1.0
What is wrong with each displacement curve in Figure P16.26?Data from P16.26 (a) (b) (c)
At \(t=0\), a wave pulse has a shape given by the timeindependent wave function\[f(x)=\frac{a}{b^{2}+x^{2}}\]where \(a=0.030 \mathrm{~m}^{3}\) and \(b=2.0 \mathrm{~m}\). (a) If the pulse travels in
A wave traveling along a string is described by\[f(x, t)=a \sin (\pi b x+q t),\]with \(a=30 \mathrm{~mm}, b=0.33 \mathrm{~m}^{-1}\), and \(q=10.47 \mathrm{~s}^{-1}\). (a) Calculate the amplitude,
A wave is described by the equation\[f(x)=a \sin (b x),\]with \(a=0.095 \mathrm{~m}\) and \(b=2.25 \mathrm{~m}^{-1}\). (a) Calculate its wavelength. (b) If the wave has a speed of \(17.0 \mathrm{~m}
As an earthquake starts, you are standing \(150 \mathrm{~km}\) (as the wave travels) from the epicenter. A geophysicist near the epicenter immediately telephones you to let you know that the
The motion of a wave traveling along an \(x\) axis is given by\[f(x, t)=a \sin [b x+q t \mid,\]with \(a=6.00 \mathrm{~m}, b=\pi \mathrm{cm}^{-1}\), and \(q=12.0 \mathrm{~s}^{-1}\). Determine the
A plucked violin string carries a traveling wave given by the equation\[f(x, t)=a \sin \left[b(x-c t)+\phi_{\mathrm{i}}\right],\]with \(a=0.00580 \mathrm{~m}, b=33.05 \mathrm{~m}^{-1}\), and \(c=245
A wave that was produced by a harmonic oscillator and is traveling along a string is described by the equation\[f(x, t)=a \sin |b(x-c t)|,\]with \(a=46 \mathrm{~mm}, b=4 \pi \mathrm{m}^{-1}\), and
The amplitude of a wave traveling on a string is \(0.250 \mathrm{~m}\). The \(80.0-\mathrm{Hz}\) wave is traveling in the positive \(x\) direction at a wave speed of \(17.5 \mathrm{~m} /
Watching your fish swim in their tank, you notice that when one fish repeatedly jumps, it causes a standing wave given by the time-independent function\[f(x)=a \sin (b x),\]with \(a=0.015
After tying one end of a rope to a stationary object, you flick the free end so as to cause a sinusoidal standing wave that has a maximum displacement of \(0.50 \mathrm{~m}\) and a wavelength of
When one end of a string is tied to a pole and the other end is moved with frequency \(f\), the standing wave pattern shown in Figure P16.37 is created. What is the smallest frequency at which the
You have two string segments of equal length, segment 1 of linear mass density \(\mu_{1}\) and segment 2 of linear mass density \(\mu_{2}>\mu_{1}\). You splice the two together and then tie the
A guitar string has a length of \(0.650 \mathrm{~m}\) and a mass of \(4.00 \times 10^{-3} \mathrm{~kg}\). (a) If it is kept under a tension of \(126 \mathrm{~N}\), what is the fundamental (smallest
The equations for two waves traveling along the same string are\[f_{1}(x, t)=a \sin (b x-q t)\]and\[f_{2}(x, t)=a \sin \left(b x+q t+\frac{1}{3} \pi\right),\]with \(a=3.00 \times 10^{-2} \mathrm{~m},
A string vibrates in a standing wave according to the function\[f(x, t)=a \sin (b x) \cos (q t),\]with \(a=6.00 \times 10^{-2} \mathrm{~m}, b=\frac{1}{3} \pi \mathrm{cm}^{-1}\), and \(q=40 \pi
A traveling wave on a long string is described by the time-dependent wave function\[f(x, t)=a \sin (b x-q t),\]with \(a=6.00 \times 10^{-2} \mathrm{~m}, b=5 \pi \mathrm{m}^{-1}\), and \(q=314
You have a trough \(3.60 \mathrm{~m}\) long. It is filled with water, and you want to create a standing wave such that a node occurs every \(0.30 \mathrm{~m}\). (a) What is the wavelength of this
Two sinusoidal waves travel along the same string. Their time-dependent wave functions are\[\begin{aligned}& f_{1}(x, t)=a \sin \left(b x-q t-\frac{1}{4} \pi\right) \\& f_{2}(x, t)=a \sin \left(b x-q

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