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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions
Oil explorers set off explosives to make loud sounds, then listen for the echoes from underground oil deposits. Geologists suspect that there is oil under 500-m-deep Lake Physics. It’s known that Lake Physics is carved out of a granite basin. Explorers detect a weak echo 0.94 s after exploding
String 1 in FIGURE P16.47 has linear density 2.0 g/m and string 2 has linear density 4.0 g/m.A student sends pulses in both directions by quickly pulling up on the knot, then releasing it.What should the string lengths L1and L2be if the pulses are to reach the ends of the strings simultaneously?
FIGURE P16.45 is a history graph at x = 0 m of a wave traveling in the positive x-direction at 4.0 m/s. a. What is the wavelength?b. What is the phase constant of the wave?c. Write the displacement equation for this wave. D (mm) -t (s) -0.1/0.1 p.2 0.3 0.4 0.5 History graph at x=0 m Wave
A mother hawk screeches as she dives at you. You recall from biology that female hawks screech at 800 Hz, but you hear the screech at 900 Hz. How fast is the hawk approaching?
A bat locates insects by emitting ultrasonic “chirps” and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?
An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 90 km/h. What is the frequency heard bya. A person standing beside the road in front of the car?b. A person on the ground behind the car?
A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25.0 m/s on a day when the speed of sound is 340 m/s.a. What frequency do you hear?b. What frequency does your friend hear if you suddenly start singing at 400 Hz?
The sound intensity level 5.0 m from a large power saw is 100 dB. At what distance will the sound be a more tolerable 80 dB?
A loudspeaker on a tall pole broadcasts sound waves equally in all directions. What is the speaker’s power output if the sound intensity level is 90 dB at a distance of 20 m?
What are the sound intensity levels for sound waves of intensity (a) 3.0 × 10-6 W/m2(b) 3.0 × 10-2 W/m2?
The sun emits electromagnetic waves with a power of 4.0 × 1026 W. Determine the intensity of electromagnetic waves from the sun just outside the atmospheres of Venus, the earth, and Mars.
During takeoff, the sound intensity level of a jet engine is 140 dB at a distance of 30 m. What is the sound intensity level at a distance of 1.0 km?
A concert loudspeaker suspended high above the ground emits 35 W of sound power. A small microphone with a 1.0 cm2 area is 50 m from the speaker.a. What is the sound intensity at the position of the microphone?b. How much sound energy impinges on the microphone each second?
The intensity of electromagnetic waves from the sun is 1.4 kW/m2 just above the earth’s atmosphere. Eighty percent of this reaches the surface at noon on a clear summer day. Suppose you think of your back as a 30 cm × 50 cm rectangle. How many joules of solar energy fall on your back as you work
A sound wave with intensity 2.0 × 10-3 W/m2 is perceived to be modestly loud. Your eardrum is 6.0 mm in diameter. How much energy will be transferred to your eardrum while listening to this sound for 1.0 min?
A sound source is located somewhere along the x-axis. Experiments show that the same wave front simultaneously reaches listeners at x = -7.0 m and x = +3.0 m.a. What is the x-coordinate of the source?b. A third listener is positioned along the positive y-axis. What is her y-coordinate if the same
A loudspeaker at the origin emits a 120 Hz tone on a day when the speed of sound is 340 m/s. The phase difference between two points on the x-axis is 5.5 rad. What is the distance between these two points?
A spherical wave with a wavelength of 2.0 m is emitted from the origin. At one instant of time, the phase at r = 4.0 m is π rad. At that instant, what is the phase at r = 3.5 m and at r = 4.5 m?
A circular wave travels outward from the origin. At one instant of time, the phase at r1 = 20 cm is 0 rad and the phase at r2 = 80 cm is 3π rad. What is the wavelength of the wave?
The density of mercury is 13,600 kg/m3. What is the speed of sound in mercury at 20°C?
What is the speed of sound in air(a) On a cold winter day in Minnesota when the temperature is –25°F, (b) On a hot summer day in Death Valley when the temperature is 125°F?
A 440 Hz sound wave in 20°C air propagates into the water of a swimming pool. What are the wave’s(a) Frequency(b) Wavelength in the water?
A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm.a. What is the speed of light in this solid?b. What is the light’s frequency in the solid?
a. How long does it take light to travel through a 3.0-mm thick piece of window glass?b. Through what thickness of water could light travel in the same amount of time?
Cell phone conversations are transmitted by high-frequency radio waves. Suppose the signal has wavelength 35 cm while traveling through air. What are the(a) Frequency(b) Wavelength as the signal travels through 3-mm-thick window glass into your room?
A hammer taps on the end of a 4.00-m-long metal bar at room temperature. A microphone at the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through the air. The pulses are separated in time by 9.00 ms. What is the speed of sound in this
a. Telephone signals are often transmitted over long distances by microwaves. What is the frequency of microwave radiation with a wavelength of 3.0 cm?b. Microwave signals are beamed between two mountaintops 50 km apart. How long does it take a signal to travel from one mountaintop to the other?
a. An FM radio station broadcasts at a frequency of 101.3 MHz. What is the wavelength?b. What is the frequency of a sound source that produces the same wavelength in 20°C air?
a. What is the frequency of blue light that has a wavelength of 450 nm?b. What is the frequency of red light that has a wavelength of 650 nm?c. What is the index of refraction of a material in which the red-light wavelength is 450 nm?
a. What is the frequency of an electromagnetic wave with a wavelength of 20 cm?b. What would be the wavelength of a sound wave in water with the same frequency as the electromagnetic wave of part a?
a. What is the wavelength of a 2.0 MHz ultrasound wave traveling through aluminum?b. What frequency of electromagnetic wave would have the same wavelength as the ultrasound wave of part a?
Show that the displacement D(x, t) = ln(ax + bt), where a and b are constants, is a solution to the wave equation. Then find an expression in terms of a and b for the wave speed.
Show that the displacement D(x, t) = cx2 + dt2, where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.
What are the amplitude, frequency, and wavelength of the wave in FIGURE EX16.14? D (cm) 6- 3- t (s) 0.2 /0.4 0.6\ 0.8 /1.0 -3- -6- History graph at x= 0 m Wave traveling left at 2.0 m/s FIGURE EX16.14
The displacement of a wave traveling in the positive x-direction is D(x, t) = (3.5 cm) sin(2.7x - 124t), where x is in m and t is in s.What are the(a) Frequency,(b) Wavelength,(c) Speed of this wave?
The displacement of a wave traveling in the negative y-direction is D(y, t) = (5.2 cm) sin(5.5y + 72t), where y is in m and t is in s.What are the (a) Frequency,(b) Wavelength,(c) Speed of this wave?
You are standing at x = 0 m, listening to a sound that is emitted at frequency f0. The graph of FIGURE Q16.12 shows the frequency you hear during a 4-second interval. Which of the following describes the sound source? Explain your choice.A. It moves from left to right and passes you at t = 2 s.B.
A wave travels with speed 200 m/s. Its wave number is 1.5 rad/m. What are its(a) Wavelength(b) Frequency?
One physics professor talking produces a sound intensity level of 52 dB. It’s a frightening idea, but what would be the sound intensity level of 100 physics professors talking simultaneously?
A wave has angular frequency 30 rad/s and wavelength 2.0 m.What are its Wave number.
Sound wave A delivers 2 J of energy in 2 s. Sound wave B delivers 10 J of energy in 5 s. Sound wave C delivers 2 mJ of energy in 1 ms. Rank in order, from largest to smallest, the sound powers PA, PB, and PC of these three sound waves. Explain.
FIGURE EX16.9 is the snapshot graph at t = 0 s of a longitudinal wave. Draw the corresponding picture of the particle positions, as was done in Figure 16.9b. Let the equilibrium spacing between the particles be 1.0 cm. Ax (cm) 0.5- Tx(cm) FIGURE EX16.9 4 6 8. 10 2.
FIGURE Q16.9 shows the wave fronts of a circular wave. What is the phase difference between(a) Points A and B(b) Points C and D(c) Points E and F? D E• A'
FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s. x (ст) FIGURE EX16.8 6. 8. 10 F00 4. 2-
FIGURE Q16.8 is a snapshot graph of a sinusoidal wave at t = 1.0 s.What is the phase constant of this wave? 1 m/s x (m) Snapshot graph at t = 1.0 s FIGURE Q16.8 4. 3. 2.
Draw the snapshot graph D(x, t = 1.0 s) at t = 1.0 s for the wave shown in FIGURE EX16.7. D (cm) - t (s) S 6 -2-1 -1| History graph of a wave at x =0 m Wave moving to the left at 1.0 m/s -2 –1 1 2 3 4 FIGURE EX16.7
What are the amplitude, wavelength, frequency, and phase constant of the traveling wave in FIGURE Q16.7? D (cm) 24 m/s 2- rX (m) 4 8 /12 16\ 20 -2. -4- Snapshot graph at t = 0 s FIGURE Q16.7
Draw the snapshot graph D(x, t = 0 s) at t = 0 s for the wave shown in FIGURE EX16.6. D (cm) t (s) 1 2 3 4 5 6 -1| -2 –1 History graph of a wave at x = 2 m Wave moving to the right at 1.0 m/s
A sound wave with wavelength λ0 and frequency f0 moves into a new medium in which the speed of sound is v1 = 2v0. What are the new wavelength λ1 and frequency f1? Explain.
Draw the history graph D(x = 0 m, t) at x = 0 m for the wave shown in FIGURE EX16.5. D (cm) 1- E1.0 m/s TX (m) 2 3 4 5 6 7 -1 -11 Snapshot graph of a wave at t=0s FIGURE EX16.5
Rank in order, from largest to smallest, the wavelengths λa, λb, and λc for sound waves having frequencies fa = 100 Hz, fb = 1000 Hz, and fc = 10,000 Hz. Explain.
Draw the history graph D(x = 4.0 m, t) at x = 4.0 m for the wave shown in FIGURE EX16.4. D (cm) 14 -x (m) 5 6 7 1 2 3 -1| 1.0 m/s» Snapshot graph of a wave at f = 2 s FIGURE EX16.4
Figure Q16.4 shows a snapshot graph and a history graph for a wave pulse on a stretched string. They describe the same wave from two perspectives.a. In which direction is the wave traveling? Explain.b. What is the speed of this wave? Snapshot at t = 0.01 s History at x = 2 cm x (ст) t (s) 0.06
A 25 g string is under 20 N of tension. A pulse travels the length of the string in 50 ms. How long is the string?
Figure Q16.3 is a history graph showing the displacement as a function of time at one point on a string. Did the displacement at this point reach its maximum of 2 mm before or after the interval of time when the displacement was a constant 1 mm? D (mm) 24 1- t (s) 0.00 0.04 0.08 FIGURE Q16.3
The wave speed on a string is 150 m/s when the tension is 75 N.What tension will give a speed of 180 m/s?
A wave pulse travels along a stretched string at a speed of 200 cm/s. What will be the speed if:a. The string’s tension is doubled?b. The string’s mass is quadrupled (but its length is unchanged)?c. The string’s length is quadrupled (but its mass is unchanged)?
The wave speed on a string under tension is 200 m/s. What is the speed if the tension is halved?
The three wave pulses in FIGURE Q16.1 travel along the same stretched string.Rank in order, from largest to smallest, their wave speeds va, vb, and vc. Explain. Va Ve
FIGURE CP15.81 shows a 200 g uniform rod pivoted at one end. The other end is attached to a horizontal spring. The spring is neither stretched nor compressed when the rod hangs straight down. What is the rod??s oscillation period? You can assume that the rod??s angle from vertical is always small.
The analysis of a simple pendulum assumed that the mass was a particle, with no size. A realistic pendulum is a small, uniform sphere of mass M and radius R at the end of a massless string, with L being the distance from the pivot to the center of the sphere.a. Find an expression for the period of
A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height 3.0 cm above the top of the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation frequency?
A uniform rod of length L oscillates as a pendulum about a pivot that is a distance x from the center.a. For what value of x, in terms of L, is the oscillation period a minimum?b. What is the minimum oscillation period of a 15 kg, 1.0-m-long steel bar?
A solid sphere of mass M and radius R is suspended from a thin rod, as shown in FIGURE CP15.77. The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency f of small angle oscillations. Pivot R
A 15@cm@long, 200 g rod is pivoted at one end. A 20 g ball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?
A block on a frictionless table is connected as shown in FIGURE P15.75 to two springs having spring constants k1and k2.Find an expression for the block€™s oscillation frequency f in terms of the frequencies f1and f2at which it would oscillate if attached to spring 1 or spring 2 alone. k1
A block on a frictionless table is connected as shown in FIGURE P15.74 to two springs having spring constants k1and k2.Show that the block€™s oscillation frequency is given by f = ˆšf12+ f22 where f1and f2are the frequencies at which it would oscillate if attached to spring
Prove that the expression for x(t) in Equation 15.55 is a solution to the equation of motion for a damped oscillator, Equation 15.54, if and only if the angular frequency ω is given by the expression in Equation 15.56.
A 200 g oscillator in a vacuum chamber has a frequency of 2.0 Hz. When air is admitted, the oscillation decreases to 60% of its initial amplitude in 50 s. How many oscillations will have been completed when the amplitude is 30% of its initial value?
A 250 g air-track glider is attached to a spring with spring constant 4.0 N/m. The damping constant due to air resistance is 0.015 kg/s. The glider is pulled out 20 cm from equilibrium and released. How many oscillations will it make during the time in which the amplitude decays to e-1 of its
A captive James Bond is strapped to a table beneath a huge pendulum made of a 2.0-m-diameter uniform circular metal blade rigidly attached, at its top edge, to a 6.0-m-long, massless rod.The pendulum is set swinging with a 10° amplitude when its lower edge is 3.0 m above the prisoner, then the
A spring with spring constant 15.0 N/m hangs from the ceiling.A 500 g ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. What is the time constant if the ball’s amplitude has decreased to 3.0 cm after 30 oscillations?
An oscillator with a mass of 500 g and a period of 0.50 s has an amplitude that decreases by 2.0% during each complete oscillation. If the initial amplitude is 10 cm, what will be the amplitude after 25 oscillations?
The 15 g head of a bobble-head doll oscillates in SHM at a frequency of 4.0 Hz. a. What is the spring constant of the spring on which the head is mounted? b. The amplitude of the head’s oscillations decreases to 0.5 cm in 4.0 s. What is the head’s damping constant?
Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x ≤ R from the center. It can be shown that the net gravitational force on the particle is due entirely to the
On your first trip to Planet X you happen to take along a 200 g mass, a 40-cm-long spring, a meter stick, and a stopwatch. You’re curious about the free-fall acceleration on Planet X, where ordinary tasks seem easier than on earth, but you can’t find this information in your Visitor’s Guide.
A penny rides on top of a piston as it undergoes vertical simple harmonic motion with an amplitude of 4.0 cm. If the frequency is low, the penny rides up and down without difficulty. If the frequency is steadily increased, there comes a point at which the penny leaves the surface.a. At what point
A molecular bond can be modeled as a spring between two atoms that vibrate with simple harmonic motion. FIGURE P15.63 shows an SHM approximation for the potential energy of an HCl molecule. Because the chlorine atom is so much more massive than the hydrogen atom, it is reasonable to assume that the
FIGURE P15.62 is a top view of an object of mass m connected between two stretched rubber bands of length L. The object rests on a frictionless surface. At equilibrium, the tension in each rubber band is T. Find an expression for the frequency of oscillations perpendicular to the rubber bands.
A 200 g block attached to a horizontal spring is oscillating with an amplitude of 2.0 cm and a frequency of 2.0 Hz. Just as it passes through the equilibrium point, moving to the right, a sharp blow directed to the left exerts a 20 N force for 1.0 ms. What are the new(a) Frequency(b) Amplitude?
A 500 g air-track glider attached to a spring with spring constant 10 N/m is sitting at rest on a frictionless air track. A 250 g glider is pushed toward it from the far end of the track at a speed of 120 cm/s. It collides with and sticks to the 500 g glider. What are the amplitude and period of
Interestingly, there have been several studies using cadavers to determine the moments of inertia of human body parts, information that is important in biomechanics. In one study, the center of mass of a 5.0 kg lower leg was found to be 18 cm from the knee.When the leg was allowed to pivot at the
A uniform rod of mass M and length L swings as a pendulum on a pivot at distance L/4 from one end of the rod. Find an expression for the frequency f of small-angle oscillations.
The pendulum shown in FIGURE P15.57 is pulled to a 10° angle on the left side and released.a. What is the period of this pendulum?b. What is the pendulum€™s maximum angle on the right side? 12 cm Peg. 12 cm
Orangutans can move by brachiation, swinging like a pendulum beneath successive handholds. If an orangutan has arms that are 0.90 m long and repeatedly swings to a 20° angle, taking one swing after another, estimate its speed of forward motion in m/s.While this is somewhat beyond the range of
It is said that Galileo discovered a basic principle of the pendulum— that the period is independent of the amplitude—by using his pulse to time the period of swinging lamps in the cathedral as they swayed in the breeze. Suppose that one oscillation of a swinging lamp takes 5.5 s.a. How long is
It has recently become possible to €œweigh€ DNA molecules by measuring the influence of their mass on a nano-oscillator. FIGURE P15.54 shows a thin rectangular cantilever etched out of silicon (density 2300 kg/m3) with a small gold dot (not visible) at the end. If pulled down
A 1.00 kg block is attached to a horizontal spring with spring constant 2500 N/m. The block is at rest on a frictionless surface. A 10 g bullet is fired into the block, in the face opposite the spring, and sticks. What was the bullet’s speed if the subsequent oscillations have an amplitude of
The two blocks in FIGURE P15.52 oscillate on a frictionless surface with a period of 1.5 s. The upper block just begins to slip when the amplitude is increased to 40 cm. What is the coefficient of static friction between the two blocks? FIGURE P15.52
A compact car has a mass of 1200 kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.a. What is the spring constant of each spring if the empty car bounces up and down 2.0 times each second?b. What will
A mass hanging from a spring oscillates with a period of 0.35 s.Suppose the mass and spring are swung in a horizontal circle, with the free end of the spring at the pivot. What rotation frequency, in rpm, will cause the spring’s length to stretch by 15%?
Scientists are measuring the properties of a newly discovered elastic material. They create a 1.5-m-long, 1.6-mm-diameter cord, attach an 850 g mass to the lower end, then pull the mass down 2.5 mm and release it. Their high-speed video camera records 36 oscillations in 2.0 s. What is Young’s
A 75 kg student jumps off a bridge with a 12-m-long bungee cord tied to his feet. The massless bungee cord has a spring constant of 430 N/m.a. How far below the bridge is the student’s lowest point?b. How long does it take the student to reach his lowest point?You can assume that the bungee cord
A block hangs in equilibrium from a vertical spring. When a second identical block is added, the original block sags by 5.0 cm.What is the oscillation frequency of the two-block system?
A 200 g block hangs from a spring with spring constant 10 N/m.At t = 0 s the block is 20 cm below the equilibrium point and moving upward with a speed of 100 cm/s. What are the block’sa. Oscillation frequency?b. Distance from equilibrium when the speed is 50 cm/s?c. Distance from equilibrium at t
A 5.0 kg block hangs from a spring with spring constant 2000 N/m. The block is pulled down 5.0 cm from the equilibrium position and given an initial velocity of 1.0 m/s back toward equilibrium.What are the(a) Frequency,(b) Amplitude,(c) Total mechanical energy of the motion?
Your lab instructor has asked you to measure a spring constant using a dynamic method€”letting it oscillate€”rather than a static method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses on the lower end, and start them oscillating.
Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then
An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk (m = 0.10 g) driven back and forth in SHM at 1.0 MHz by an electromagnetic coil.a. The maximum restoring force that can be applied to the disk without breaking it is 40,000 N. What is the maximum
A 0.300 kg oscillator has a speed of 95.4 cm/s when its displacement is 3.00 cm and 71.4 cm/s when its displacement is 6.00 cm. What is the oscillator’s maximum speed?
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