Is the displacement D1x, t2 = 10.10 - 0.10x2 + xt - 2.5t 2

What is a wave?

What are some wave properties?

Are sound and light waves?

Do waves carry energy?

What is the Doppler effect?

How will I use waves?

A 2.00-m-long metal wire is attached to a motion sensor, stretched horizontally to a pulley 1.50 m away, then connected to a 2.00 kg hanging mass that provides tension. A mechanical pick plucks a horizontal segment of wire right at the pulley, creating a small wave pulse that travels along the wire. The plucking motion starts a timer that is stopped by the motion sensor when the pulse reaches the end of the wire. What is the wires linear density if the pulse takes 18.0 ms to travel the length of the wire?

Which of the following actions would make a pulse travel faster along a stretched string? More than one answer may be correct. If so, give all that are correct. a. Move your hand up and down more quickly as you generate the pulse. b. Move your hand up and down a larger distance as you generate the pulse. c. Use a heavier string of the same length, under the same tension. d. Use a lighter string of the same length, under the same tension. e. Stretch the string tighter to increase the tension. f. Loosen the string to decrease the tension. g. Put more force into the wave.

FIGURE 16.7 is a snapshot graph at t = 0 s of a wave moving to the right at a speed of 2.0 m/s. Draw a history graph for the position x = 8.0 m

The graph at the right is the history graph at x = 4.0 m of a wave traveling to the right at a speed of 2.0 m/s. Which is the history graph of this wave at x = 0 m?

What is the frequency of this traveling wave? a. 0.1 Hz b. 0.2 Hz c. 2 Hz d. 5 Hz e. 10 Hz f. 500 Hz

A sinusoidal wave with an amplitude of 1.00 cm and a frequency of 100 Hz travels at 200 m/s in the positive x-direction. At t = 0 s, the point x = 1.00 m is on a crest of the wave. a. Determine the values of A, v, l, k, f, v, T, and f0 for this wave. b. Write the equation for the waves displacement as it travels. c. Draw a snapshot graph of the wave at t = 0 s.

A very long string with m = 2.0 g/m is stretched along the x-axis with a tension of 5.0 N. At x = 0 m it is tied to a 100 Hz simple harmonic oscillator that vibrates perpendicular to the string with an amplitude of 2.0 mm. The oscillator is at its maximum positive displacement at t = 0 s. a. Write the displacement equation for the traveling wave on the string. b. At t = 5.0 ms, what is the strings displacement at a point 2.7 m from the oscillator?

A light wave travels from left to right through three transparent materials of equal thickness. Rank in order, from largest to smallest, the indices of refraction na, nb, and nc

A satellite exploring Jupiter transmits data to the earth as a radio wave with a frequency of 200 MHz. What is the wavelength of the electromagnetic wave, and how long does it take the signal to travel 800 million kilometers from Jupiter to the earth?

What is the phase difference between the crest of a wave and the adjacent trough? a. -2p rad b. 0 rad c. p/4 rad d. p/2 rad e. p rad f. 3p rad

Orange light with a wavelength of 600 nm is incident upon a 1.00-mm-thick glass microscope slide. a. What is the light speed in the glass? b. How many wavelengths of the light are inside the slide?

Four trumpet players are playing the same note. If three of them suddenly stop, the sound intensity level decreases by a. 40 dB b. 12 dB c. 6 dB d. 4 dB

Predict the speed of sound in water at 20C.

Amy and Zack are both listening to the source of sound waves that is moving to the right. Compare the frequencies each hears. a. fAmy 7 fZack b. fAmy = fZack c. fAmy 6 fZack

A 100 Hz sound wave travels with a wave speed of 343 m/s. a. What is the phase difference between two points 60.0 cm apart along the direction the wave is traveling? b. How far apart are two points whose phase differs by 90?

A typical red laser pointer emits 1.0 mW of light power into a 1.0-mm-diameter laser beam. What is the intensity of the laser beam?

The blender making a smoothie produces a sound intensity level of 83 dB. What is the intensity of the sound? What will the sound intensity level be if a second blender is turned on?

A police siren has a frequency of 550 Hz as the police car approaches you, 450 Hz after it has passed you and is receding. How fast are the police traveling? The temperature is 20C.

Hydrogen atoms in the laboratory emit red light with wavelength 656 nm. In the light from a distant galaxy, this spectral line is observed at 691 nm. What is the speed of this galaxy relative to the earth?

The loudspeaker on a homecoming floatmounted on a poleis stuck playing an annoying 210 Hz tone. When the speaker is 10 m away, you measure the sound to be a loud 95 dB at 208 Hz. How long will it take for the sound intensity level to drop to a tolerable 55 dB?

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.

A wave pulse travels along a stretched string at a speed of 200 cm/s. What will be the speed if: a. The strings tension is doubled? b. The strings mass is quadrupled (but its length is unchanged)? c. The strings length is quadrupled (but its mass is unchanged)? Note: Each part is independent and refers to changes made to the original 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?

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?

Rank in order, from largest to smallest, the wavelengths la, lb, and lc for sound waves having frequencies fa = 100 Hz, fb = 1000 Hz, and fc = 10,000 Hz. Explain

A sound wave with wavelength l0 and frequency f0 moves into a new medium in which the speed of sound is v1 = 2v0. What are the new wavelength l1 and frequency f1? Explain

What are the amplitude, wavelength, frequency, and phase constant of the traveling wave in FIGURE Q16.7?

FIGURE Q16.8 is a snapshot graph of a sinusoidal wave at t = 1.0 s. What is the phase constant of this wave?

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, and (c) points E and F?

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.

One physics professor talking produces a sound intensity level of 52 dB. Its a frightening idea, but what would be the sound intensity level of 100 physics professors talking simultaneously?

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. It moves from right to left and passes you at t = 2 s. C. It moves toward you but doesnt reach you. It then reverses direction at t = 2 s. D. It moves away from you until t = 2 s. It then reverses direction and moves toward you but doesnt reach you.

The wave speed on a string under tension is 200 m/s. What is the speed if the tension is halved?

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 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?

Draw the history graph D1x = 4.0 m, t2 at x = 4.0 m for the wave shown in FIGURE EX16.4.

Draw the history graph D1x = 0 m, t2 at x = 0 m for the wave shown in FIGURE EX16.5.

Draw the snapshot graph D1x, t = 0 s2 at t = 0 s for the wave shown in FIGURE EX16.6.

Draw the snapshot graph D1x, t = 1.0 s2 at t = 1.0 s for the wave shown in FIGURE EX16.7

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 D1x, t = 0 s2 of this wave at t = 0 s.

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.

A wave has angular frequency 30 rad/s and wavelength 2.0 m. What are its (a) wave number and (b) wave speed?

A wave travels with speed 200 m/s. Its wave number is 1.5 rad/m. What are its (a) wavelength and (b) frequency?

The displacement of a wave traveling in the negative y-direction is D1y, t2 = 15.2 cm2 sin15.5y + 72t2, where y is in m and t is in s. What are the (a) frequency, (b) wavelength, and (c) speed of this wav

The displacement of a wave traveling in the positive x-direction is D1x, t2 = 13.5 cm2 sin12.7x - 124t2, where x is in m and t is in s. What are the (a) frequency, (b) wavelength, and (c) speed of this wave?

What are the amplitude, frequency, and wavelength of the wave in FIGURE EX16.14?

Show that the displacement D1x, t2 = cx2 + dt 2 , 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

Show that the displacement D1x, t2 = ln1ax + bt2, 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.

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?

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 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. 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 20C air?

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 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 metal?

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 and (b) wavelength as the signal travels through 3-mm-thick window glass into your room?

a. How long does it take light to travel through a 3.0-mmthick piece of window glass? b. Through what thickness of water could light travel in the same amount of time?

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 lights frequency in the solid?

A 440 Hz sound wave in 20C air propagates into the water of a swimming pool. What are the waves (a) frequency and (b) wavelength in the water?

What is the speed of sound in air (a) on a cold winter day in Minnesota when the temperature is 25F, and (b) on a hot summer day in Death Valley when the temperature is 125F?

The density of mercury is 13,600 kg/m3 . What is the speed of sound in mercury at 20C?

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 3p rad. What is the wavelength of the wave?

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 p rad. At that instant, what is the phase at r = 3.5 m and at r = 4.5 m?

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 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 wave front reaches her at the same instant it does the first two listeners?

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?

The intensity of electromagnetic waves from the sun is 1.4 kW/m2 just above the earths 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 on your tan for 1.0 h

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?

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?

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.

What are the sound intensity levels for sound waves of intensity (a) 3.0 * 10-6 W/m2 and (b) 3.0 * 10-2 W/m2 ?

A loudspeaker on a tall pole broadcasts sound waves equally in all directions. What is the speakers power output if the sound intensity level is 90 dB at a distance of 20 m?

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 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?

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 by a. A person standing beside the road in front of the car? b. A person on the ground behind the car?

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?

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?

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

FIGURE P16.46 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left. a. What is the wave speed? b. What is the phase constant of the wave? c. Write the displacement equation for this wave

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 L1 and L2 be if the pulses are to reach the ends of the strings simultaneously?

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. Its known that Lake Physics is carved out of a granite basin. Explorers detect a weak echo 0.94 s after exploding dynamite at the lake surface. If

One cue your hearing system uses to localize a sound (i.e., to tell where a sound is coming from) is the slight difference in the arrival times of the sound at your ears. Your ears are spaced approximately 20 cm apart. Consider a sound source 5.0 m from the center of your head along a line 45 to your right. What is the difference in arrival times? Give your answer in microseconds. Hint: You are looking for the difference between two numbers that are nearly the same. What does this near equality imply about the necessary precision during intermediate stages of the calculation?

A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Earthquakes are essentially sound wavescalled seismic wavestraveling through the earth. Because the earth is solid, it can support both longitudinal and transverse seismic waves. The speed of longitudinal waves, called P waves, is 8000 m/s. Transverse waves, called S waves, travel at a slower 4500 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 2.0 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Helium (density 0.18 kg/m3 at 0C and 1 atm pressure) remains a gas until the extraordinarily low temperature of 4.2 K. What is the speed of sound in helium at 5 K?

A 20.0-cm-long, 10.0-cm-diameter cylinder with a piston at one end contains 1.34 kg of an unknown liquid. Using the piston to compress the length of the liquid by 1.00 mm increases the pressure by 41.0 atm. What is the speed of sound in the liquid?

A sound wave is described by D1y, t2 = 10.0200 mm2 * sin318.96 rad/m2y + 13140 rad/s2t + p/4 rad4, where y is in m and t is in s. a. In what direction is this wave traveling? b. Along which axis is the air oscillating? c. What are the wavelength, the wave speed, and the period of oscillation?

A wave on a string is described by D1x, t2 = 13.0 cm2 * sin32p1x/12.4 m2 + t/10.20 s2 + 124, where x is in m and t is in s. a. In what direction is this wave traveling? b. What are the wave speed, the frequency, and the wave number? c. At t = 0.50 s, what is the displacement of the string at x = 0.20 m?

A wave on a string is described by D1x, t2 = 12.00 cm2 * sin3112.57 rad/m2x - 1638 rad/s2t4, where x is in m and t in s. The linear density of the string is 5.00 g/m. What are a. The string tension? b. The maximum displacement of a point on the string? c. The maximum speed of a point on the string?

FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string?

FIGURE P16.58 shows two masses hanging from a steel wire. The mass of the wire is 60.0 g. A wave pulse travels along the wire from point 1 to point 2 in 24.0 ms. What is mass m?

A wire is made by welding together two metals having different densities. FIGURE P16.59 shows a 2.00-m-long section of wire centered on the junction, but the wire extends much farther in both directions. The wire is placed under 2250 N tension, then a 1500 Hz wave with an amplitude of 3.00 mm is sent down the wire. How many wavelengths (complete cycles) of the wave are in this 2.00-m-long section of the wire?

The string in FIGURE P16.60 has linear density m. Find an expression in terms of M, m, and u for the speed of waves on the string.

A string that is under 50.0 N of tension has linear density 5.0 g/m. A sinusoidal wave with amplitude 3.0 cm and wavelength 2.0 m travels along the string. What is the maximum speed of a particle on the string?

The G string on a guitar is a 0.46-mm-diameter steel string with a linear density of 1.3 g/m. When the string is properly tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning is done by turning the tuning screw, which slowly tightensand stretchesthe string. By how many mm does a 75-cm-long G string stretch when its first tuned?

A sinusoidal wave travels along a stretched string. A particle on the string has a maximum speed of 2.0 m/s and a maximum acceleration of 200 m/s2 . What are the frequency and amplitude of the wave?

Is the displacement D1x, t2 = 10.10 - 0.10x2 + xt - 2.5t 2 2 m, where x is in m and t is in s, a possible traveling wave? If so, what is the wave speed?

Is the displacement D1x, t2 = 13.0 mm2 ei12.0x+8.0t+5.02 , where x is in m, t is in s, and i = 1-1, a possible traveling wave? If so, what is the wave speed? Complex exponentials are often used to represent waves in more advanced treatments.

An AM radio station broadcasts with a power of 25 kW at a frequency of 920 kHz. Estimate the intensity of the radio wave at a point 10 km from the broadcast antenna

LASIK eye surgery uses pulses of laser light to shave off tissue from the cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mJ of light energy. a. What is the power of one laser pulse? b. During the very brief time of the pulse, what is the intensity of the light wave?

The sound intensity 50 m from a wailing tornado siren is 0.10 W/m2 . a. What is the intensity at 1000 m? b. The weakest intensity likely to be heard over background noise is 1 mW/m2 . Estimate the maximum distance at which the siren can be heard.

A distant star system is discovered in which a planet with twice the radius of the earth and rotating 3.0 times as fast as the earth orbits a star with a total power output of 6.8 * 1029 W. a. If the stars radius is 6.0 times that of the sun, what is the electromagnetic wave intensity at the surface? Astronomers call this the surface flux. Astronomical data are provided inside the back cover of the book. b. Every planet-day (one rotation), the planet receives 9.4 * 1022 J of energy. What is the planets distance from its star? Give your answer in astronomical units (AU), where 1 AU is the distance of the earth from the sun.

A compact sound source radiates 25 W of sound energy uniformly in all directions. What is the ratio of the sound intensity at a distance of 1.0 m to that at 5.0 m in (a) a two-dimensional universe, (b) our normal three-dimensional universe, and (c) a hypothetical four-dimensional universe?

A loudspeaker, mounted on a tall pole, is engineered to emit 75% of its sound energy into the forward hemisphere, 25% toward the back. You measure an 85 dB sound intensity level when standing 3.5 m in front of and 2.5 m below the speaker. What is the speakers power output?

Your ears are sensitive to differences in pitch, but they are not very sensitive to differences in intensity. You are not capable of detecting a difference in sound intensity level of less than 1 dB. By what factor does the sound intensity increase if the sound intensity level increases from 60 dB to 61 dB?

The intensity of a sound source is described by an inversesquare law only if the source is very small (a point source) and only if the waves can travel unimpeded in all directions. For an extended source or in a situation where obstacles absorb or reflect the waves, the intensity at distance r can often be expressed as I = cPsource /r x , where c is a constant and the exponent xwhich would be 2 for an ideal spherical wavedepends on the situation. In one such situation, you use a sound meter to measure the sound intensity level at different distances from a source, acquiring the data in the table. Use the best-fit line of an appropriate graph to determine the exponent x that characterizes this sound source.

A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm. What are the highest and lowest frequencies heard by a student in the classroom?

An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a large bat to fly toward her from the back of the stage. The bat will be outfitted with a microphone to pick up the singers voice and a loudspeaker to rebroadcast the sound toward the audience. The composer wants the sound the audience hears from the bat to be, in musical terms, one half-step higher in frequency than the note they are hearing from the singer. Two notes a half-step apart have a frequency ratio of 21/12 = 1.059. With what speed must the bat fly toward the singer?

A loudspeaker on a pole is radiating 100 W of sound energy in all directions. You are walking directly toward the speaker at 0.80 m/s. When you are 20 m away, what are (a) the sound intensity level and (b) the rate (dB/s) at which the sound intensity level is increasing? Hint: Use the chain rule and the relationship log10 x = ln x/ln 10.

Show that the Doppler frequency f- of a receding source is f- = f0/11 + vs/v2.

A starship approaches its home planet at a speed of 0.10c. When it is 54 * 106 km away, it uses its green laser beam 1l = 540 nm2 to signal its approach. a. How long does the signal take to travel to the home planet? b. At what wavelength is the signal detected on the home planet

Wavelengths of light from a distant galaxy are found to be 0.50% longer than the corresponding wavelengths measured in a terrestrial laboratory. Is the galaxy approaching or receding from the earth? At what speed?

You have just been pulled over for running a red light, and the police officer has informed you that the fine will be $250. In desperation, you suddenly recall an idea that your physics professor recently discussed in class. In your calmest voice, you tell the officer that the laws of physics prevented you from knowing that the light was red. In fact, as you drove toward it, the light was Doppler shifted to where it appeared green to you. OK, says the officer, Then Ill ticket you for speeding. The fine is $1 for every 1 km/h over the posted speed limit of 50 km/h.< How big is your fine? Use 650 nm as the wavelength of red light and 540 nm as the wavelength of green light.

One way to monitor global warming is to measure the average temperature of the ocean. Researchers are doing this by measuring the time it takes sound pulses to travel underwater over large distances. At a depth of 1000 m, where ocean temperatures hold steady near 4C, the average sound speed is 1480 m/s. Its known from laboratory measurements that the sound speed increases 4.0 m/s for every 1.0C increase in temperature. In one experiment, where sounds generated near California are detected in the South Pacific, the sound waves travel 8000 km. If the smallest time change that can be reliably detected is 1.0 s, what is the smallest change in average temperature that can be measured?

A rope of mass m and length L hangs from a ceiling. a. Show that the wave speed on the rope a distance y above the lower end is v = 1gy. b. Show that the time for a pulse to travel the length of the string is t = 22L/g

A communications truck with a 44-cm-diameter dish receiver on the roof starts out 10 km from its base station. It drives directly away from the base station at 50 km/h for 1.0 h, keeping the receiver pointed at the base station. The base station antenna broadcasts continuously with 2.5 kW of power, radiated uniformly in all directions. How much electromagnetic energy does the trucks dish receive during that 1.0 h?

Some modern optical devices are made with glass whose index of refraction changes with distance from the front surface. FIGURE CP16.84 shows the index of refraction as a function of the distance into a slab of glass of thickness L. The index of refraction increases linearly from n1 at the front surface to n2 at the rear surface. a. Find an expression for the time light takes to travel through this piece of glass. b. Evaluate your expression for a 1.0-cm-thick piece of glass for which n1 = 1.50 and n2 = 1.60.

A water wave is a shallow-water wave if the water depth d is less than l/10. It is shown in hydrodynamics that the speed of a shallow-water wave is v = 1gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 100 m, are shallow-water waves when the water depth is less than 10 m. Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of 5.0 m at a distance of 100 m. How long does it take a wave to move the last 100 m to the shore? Assume that the waves are so small that they dont break before reaching the shore.