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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

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
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
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
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
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,
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
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 =
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
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?
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
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
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 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
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
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
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
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
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 =
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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?
A 100 g block attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5.0 cm.a. What is the amplitude of oscillation?b.
For a particle in simple harmonic motion, show that vmax = (π/2)vavg, where vavg is the average speed during one cycle of the motion.
a. When the displacement of a mass on a spring is 1/2 A, what fraction of the energy is kinetic energy and what fraction is potential energy?b. At what displacement, as a fraction of A, is the energy
The motion of a particle is given by x(t) = (25 cm)cos(10 t), where t is in s. What is the first time at which the kinetic energy is twice the potential energy?
A 350 g mass on a 45-cm-long string is released at an angle of 4.5° from vertical. It has a damping constant of 0.010 kg/s. After 25 s,(a) How many oscillations has it completed(b) How much energy
Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball in its socket. If the mass of the eyeball is 7.5 g, a typical value,
In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it.
The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant?
A 2.0 g spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the
A uniform steel bar swings from a pivot at one end with a period of 1.2 s. How long is the bar?
A 100 g mass on a 1.0-m-long string is pulled 8.0° to one side and released. How long does it take for the pendulum to reach 4.0° on the opposite side?
Astronauts on the first trip to Mars take along a pendulum that has a period on earth of 1.50 s. The period on Mars turns out to be 2.45 s. What is the free-fall acceleration on Mars?
What is the period of a 1.0-m-long pendulum on(a) The earth(b) Venus?
What is the length of a pendulum whose period on the moon matches the period of a 2.0-m-long pendulum on the earth?
A mass on a string of unknown length oscillates as a pendulum with a period of 4.0 s. What is the period ifa. The mass is doubled?b. The string length is doubled?c. The string length is halved?d. The
A 200 g ball is tied to a string. It is pulled to an angle of 8.0° and released to swing as a pendulum. A student with a stopwatch finds that 10 oscillations take 12 s. How long is the string?
A grandfather clock ticks each time the pendulum passes through the lowest point. If the pendulum is modeled as a simple pendulum, how long must it be for the ticks to occur once a second?
A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.0 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. What is
A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30
A spring is hanging from the ceiling. Attaching a 500 g physics book to the spring causes it to stretch 20 cm in order to come to equilibrium.a. What is the spring constant?b. From equilibrium, the
FIGURE EX15.20 is a kinetic-energy graph of a mass oscillating on a very long horizontal spring. What is the spring constant? K (J) 8. 4 x (m) FIGURE EX15.20
A student is bouncing on a trampoline. At her highest point, her feet are 55 cm above the trampoline. When she lands, the trampoline sags 15 cm before propelling her back up. For how long is she in
A 1.0 kg block is attached to a spring with spring constant 16 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 40 cm/s.What
The position of a 50 g oscillating mass is given by x(t) = (2.0 cm) cos(10 t - π/4), where t is in s. Determine:a. The amplitude.b. The period.c. The spring constant.d. The phase constant.e. The
200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -30 cm/s. Determine:a. The period.b. The angular frequency.c. The
A 200 g air-track glider is attached to a spring. The glider is pushed in 10 cm and released. A student with a stopwatch finds that 10 oscillations take 12.0 s. What is the spring constant?
A block attached to a spring with unknown spring constant oscillates with a period of 2.0 s. What is the period ifa. The mass is doubled?b. The mass is halved?c. The amplitude is doubled?d. The
An air-track glider attached to a spring oscillates with a period of 1.5 s. At t = 0 s the glider is 5.00 cm left of the equilibrium position and moving to the right at 36.3 cm/s.a. What is the phase

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