Write the y-equation for a wave traveling in the negative

Problem 1CQ a. In your own words, define what a transverse wave is. b. Give an example of a wave that, from your own experience, you know is a transverse wave. What observations or evidence tells you this is a transverse wave?

Problem 1P The wave speed on a string under tension is 200 m/s. What is the speed if the tension is doubled?

Problem 2CQ a. In your own words, define what a longitudinal wave is. b. Give an example of a wave that, from your own experience, you know is a longitudinal wave. What observations or evidence tells you this is a longitudinal wave?

Problem 2P The wave speed on a string is 150 m/s when the tension is 75.0 N. What tension will give a speed of 180 m/s?

Problem 3CQ The wave pulses shown in Figure Q15.3 travel along the same string. Rank in order, from largest to smallest, their wave speeds . Explain.

Problem 3P A wave travels along a string at a speed of 280 m/s. What will be the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?

Problem 4CQ Step-by-step solution Step 1 of 1 PREPARE: we use the concept of the speed of sound at particular temperature in air is constant.

Problem 4P The back wall of an auditorium is 26.0 m from the stage. If you are seated in the middle row, how much time elapses between a sound from the stage reaching your ear directly and the same sound reaching your ear after reflecting from the back wall?

Problem 5CQ A wave pulse travels along a 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)? d. The string’s mass and length are both quadrupled? Note that parts a–d are independent and refer to changes made to the original string.

Problem 5P 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 11.0 ms. What is the speed of sound in this metal?

Problem 6CQ An ultrasonic range finder sends out a pulse of ultrasound and measures the time between the emission of the pulse and the return of an echo from an object. This time is used to determine the distance to the object. To get good accuracy from the device, a user must enter the air temperature in the room. Why is this?

Problem 6P In an early test of sound propagation through the ocean, an underwater explosion of 1 pound of dynamite in the Bahamas was detected 3200 km away on the coast of Africa. How much time elapsed between the explosion and the detection?

Problem 7CQ A thermostat on the wall of your house keeps track of the air temperature. This simple approach is of little use in the large volume of a covered sports stadium, but there are systems that determine an average temperature of the air in a stadium by measuring the time delay between the emission of a pulse of sound on one side of the stadium and its detection on the other. Explain how such a system works.

Problem 7P Figure P15.9 is a snapshot graph of a wave at t = 0 s. Draw the history graph for this wave at x = 6 m, for t = 0 s to 6 s.

Problem 8CQ When water freezes, the density decreases and the bonds between molecules become stronger. Do you expect the speed of sound to be greater in liquid water or in water ice?

Problem 8P Figure P15.10 is a snapshot graph of a wave at t = 2 s. Draw the history graph for this wave at x = 0 m, for t = 0 s to 8 s.

Problem 9CQ Figure Q15.9 shows a history graph of the motion of one point on a string as a wave traveling to the left passes by. Sketch a snapshot graph for this wave.

Problem 9P Figure P15.11 is a history graph at x = 0 m of a wave moving to the right at 1 m/s. Draw a snapshot graph of this wave at t = 1 s.

Problem 10CQ Figure Q15.10 shows a history graph and a snapshot graph for a wave pulse on a 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?

Problem 10P Figure P15.12 is a history graph at x = 2 m of a wave moving to the left at 1 m/s. Draw the snapshot graph of this wave at t = 0 s.

Problem 11P A sinusoidal wave has period 0.20 s and wavelength 2.0 m. What is the wave speed?

Problem 11CQ Rank in order, from largest to smallest, the wavelengths for sound waves having frequencies . Explain

Problem 12CQ Explain why there is a factor of 2? in Equation 15.5.

Problem 12P A sinusoidal wave travels with speed 200 m/s. Its wavelength is 4.0 m. What is its frequency?

Problem 13CQ Bottlenose dolphins use echolocation pulses with a frequency of about 100 kHz, higher than the frequencies used by most bats. Why might you expect these water-dwelling creatures to use higher echolocation frequencies than bats?

Problem 13P The motion detector used in a physics lab sends and receives 40 kHz ultrasonic pulses. A pulse goes out, reflects off the object being measured, and returns to the detector. The lab temperature is 20°C. a. What is the wavelength of the waves emitted by the motion detector? b. How long does it take for a pulse that reflects off an object 2.5 m away to make a round trip?

Problem 14CQ A laser beam has intensity . a. What is the intensity, in terms of , if a lens focuses the laser beam to 1/10 its initial diameter? b. What is the intensity, in terms of , if a lens defocuses the laser beam to 10 times its initial diameter?

Problem 14P The displacement of a wave traveling in the positive x-direction is y (x, t) = (3.5 cm) cos (2.7x - 92t), where x is in m and t is in s. What are the (a) frequency, (b) wavelength, and (c) speed of this wave?

Problem 15CQ 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 waves. Explain.

Problem 15P The displacement of a wave traveling in the negative x-direction is y(x, t) = (5.2 cm)cos(5.5x + 72t), where x is in m and t is in s. What are the (a) frequency, (b) wavelength, and (c) speed of this wave?

Problem 16P A traveling wave has displacement given by y (x, t) = (2.0 cm) × cos (2?x - 4?t), where x is measured in cm and t in s. a. Draw a snapshot graph of this wave at t = 0 s . b. On the same set of axes, use a dotted line to show the snapshot graph of the wave at t = 1/8 s . c. What is the speed of the wave?

Problem 16CQ When you want to “snap” a towel, the best way to wrap the towel is so that the end that you hold and shake is thick, and the far end is thin. When you shake the thick end, a wave travels down the towel. How does wrapping the towel in a tapered shape help make for a good snap? Hint: Think about the speed of the wave as it moves down the towel.

Problem 17CQ The volume control on your stereo is likely designed so that each time you turn it by one click, the loudness increases by a certain number of dB. Does each click increase the output power by a fixed amount as well?

Problem 17P Figure P15.18 is a snapshot graph of a wave at t = 0 s. What are the amplitude, wavelength, and frequency of this wave?

Problem 18CQ A bullet can travel at a speed of over 1000 m/s. When a bullet is fired from a rifle, the actual firing makes a distinctive sound, but people at a distance may hear a second, different sound that is even louder. Explain the source of this sound.

Problem 18P Figure P15.19 is a history graph at x = 0 m of a wave moving to the right at 2 m/s. What are the amplitude, frequency, and wavelength of this wave?

Problem 19P A boat is traveling at 4.0 m/s in the same direction as an ocean wave of wavelength 30 m and speed 6.8 m/s. If the boat is on the crest of a wave, how much time will elapse until the boat is next on a crest?

Problem 19CQ You are standing at x = 0 m, listening to seven identical sound sources described by Figure Q15.18 . At t = 0 s, all seven are at x = 343 m and moving as shown below. The sound from all seven will reach your ear at t = 1 s. Rank in order, from highest to lowest, the seven frequencies that you hear at t = 1 s. Explain.

Problem 20MCQ Denver, Colorado, has an oldies station that calls itself “KOOL 105.” This means that they broadcast radio waves at a frequency of 105 MHz. Suppose that they decide to describe their station by its wavelength (in meters), instead of by its frequency. What name would they now use? A. KOOL 0.35 B. KOOL 2.85 C. KOOL 3.5 D. KOOL 285

Problem 20P In the deep ocean, a water wave with wavelength 95 m travels at 12 m/s. Suppose a small boat is at the crest of this wave, 1.2 m above the equilibrium position. What will be the vertical position of the boat 5.0 s later?

Problem 21MCQ What is the frequency of blue light with a wavelength of 400 nm?

Problem 21P A dolphin emits ultrasound at 100 kHz and uses the timing of reflections to determine the position of objects in the water. What is the wavelength of this ultrasound?

Problem 22MCQ Ultrasound can be used to deliver energy to tissues for therapy. It can penetrate tissue to a depth approximately 200 times its wavelength. What is the approximate depth of penetration of ultrasound at a frequency of 5.0 MHz? A. 0.29 mm B. 1.4 cm C. 6.2 cm D. 17 cm

Problem 22P 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?

Problem 23MCQ A sinusoidal wave traveling on a string has a period of 0.20 s, a wavelength of 32 cm, and an amplitude of 3 cm. The speed of this wave is A. 0.60 cm/s . B. 6.4 cm/s. C. 15 cm/s. D. 160 cm/s .

Problem 23P a. At 20°C, what is the frequency of a sound wave in air with a wavelength of 20 cm? ________________ b. What is the frequency of an electromagnetic wave with a wavelength of 20 cm? ________________ c. What would be the wavelength of a sound wave in water that has the same frequency as the electromagnetic wave of part b?

Problem 24P 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?

Problem 24MCQ Two strings of different linear density are joined together and pulled taut. A sinusoidal wave on these strings is traveling to the right, as shown in Figure Q15.24 . When the wave goes across the boundary from string 1 to string 2, the frequency is unchanged. What happens to the velocity? A. The velocity increases. B. The velocity stays the same. C. The velocity decreases.

Problem 25MCQ You stand at x = 0 m, listening to a sound that is emitted at frequency . Figure Q15.25 shows the frequency you hear during a four-second interval. Which of the following describes the motion of the sound source? 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 doesn’t 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 doesn’t reach you.

Problem 25P 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?

Problem 26P 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?

Problem 28P At a rock concert, the sound intensity 1.0 m in front of the bank of loudspeakers is . A fan is 30 m from the loud speakers. Her eardrums have a diameter of 8.4 mm. How much sound energy is transferred to each eardrum in 1.0 second?

Problem 27P Sound is detected when a sound wave causes the eardrum to vibrate (see Figure 14.26). Typically, the diameter of the eardrum is about 8.4 mm in humans. When someone speaks to you in a normal tone of voice, the sound intensity at your ear is approximately . How much energy is delivered to your eardrum each second?

Problem 29P The intensity of electromagnetic waves from the sun is just above the earth’s atmosphere. Eighty percent of this reaches the surface at noon on a clear summer day. Suppose you model 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?

Problem 30P The sun emits electromagnetic waves with a power of . Determine the intensity of electromagnetic waves from the sun just outside the atmospheres of (a) Venus, (b) Mars, and (c) Saturn. Refer to the table of astronomical data inside the back cover.

Problem 31P A large solar panel on a spacecraft in Earth orbit produces 1.0 kW of power when the panel is turned toward the sun. What power would the solar cell produce if the spacecraft were in orbit around Saturn, 9.5 times as far from the sun?

Problem 32P Solar cells convert the energy of incoming light to electric energy; a good quality cell operates at an efficiency of 15%. Each person in the United States uses energy (for lighting, heating, transportation, etc.) at an average rate of 11 kW. Although sunlight varies with season and time of day, solar energy falls on the United States at an average intensity of . Assuming you live in an average location, what total solar-cell area would you need to provide all of your energy needs with energy from the sun?

Problem 33P 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?

Problem 34P What is the sound intensity level of a sound with an intensity of ?

Problem 35P What is the sound intensity of a whisper at a distance of ? What is the corresponding sound intensity level in dB?

Problem 36P You hear a sound at 65 dB. What is the sound intensity level if the intensity of the sound is doubled?

Problem 37P The sound intensity from a jack hammer breaking concrete is at a distance of 2.0 m from the point of impact. This is sufficiently loud to cause permanent hearing damage if the operator doesn’t wear ear protection. What are (a) the sound intensity and (b) the sound intensity level for a person watching from 50 m away?

Problem 38P A concert loudspeaker suspended high off the ground emits 35 W of sound power. A small microphone with a area is 50 m from the speaker. What are (a) the sound intensity and (b) the sound intensity level at the position of the microphone?

Problem 39P A rock band playing an outdoor concert produces sound at 120 dB 5.0 m away from their single working loudspeaker. What is the sound intensity level 35 m from the speaker?

Problem 40P 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?

Problem 41P 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 standing beside the road behind the car?

Problem 42P An osprey’s call is a distinct whistle at 2200 Hz. An osprey calls while diving at you, to drive you away from her nest. You hear the call at 2300 Hz. How fast is the osprey approaching?

Problem 43P A whistle you use to call your hunting dog has a frequency of 21 kHz, but your dog is ignoring it. You suspect the whistle may not be working, but you can’t hear sounds above 20 kHz. To test it, you ask a friend to blow the whistle, then you hop on your bicycle. In which direction should you ride (toward or away from your friend) and at what minimum speed to know if the whistle is working?

Problem 44P A friend of yours is loudly singing a single note at 400 Hz while driving 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?

Problem 45P While anchored in the middle of a lake, you count exactly three waves hitting your boat every 10 s. You raise anchor and start motoring slowly in the same direction the waves are going. When traveling at 1.5 m/s, you notice that exactly two waves are hitting the boat from behind every 10 s. What is the speed of the waves on the lake?

Problem 46P A Doppler blood flow unit emits ultrasound at 5.0 MHz. What is the frequency shift of the ultrasound reflected from blood moving in an artery at a speed of 0.20 m/s?

Problem 47GP You’re watching a carpenter pound a nail. He hits the nail twice a second, but you hear the sound of the strike when his hammer is fully raised. What is the minimum distance from you to the carpenter? Assume the air temperature is 20°C.

Problem 48GP A 2.50 kHz sound wave is transmitted through an aluminum rod. a. What is its wavelength in the aluminum? ________________ b. What is the sound wave’s frequency when it passes into the air? ________________ c. What is its wavelength in air?

Problem 49GP 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 dynamite at the lake surface. If it’s really oil, how deep will they have to drill into the granite to reach it?

Problem 50GP A 2.0-m-long string is under 20 N of tension. A pulse travels the length of the string in 50 ms. What is the mass of the string?

Problem 51GP A stout cord is stretched between two fixed supports. You vigorously shake one end of the string and send a sinusoidal wave of wavelength 4.0 m along it at 16 m/s. The amplitude of the motion is 2.0 cm. What are the maximum speed and maximum acceleration of a point on the string as the wave passes?

Problem 52GP A female orb spider has a mass of 0.50 g. She is suspended from a tree branch by a 1.1 ? length of 0.0020-mm-diameter silk. Spider silk has a density of . If you tap the branch and send a vibration down the thread, how long does it take to reach the spider?

Problem 53GP Andy (mass 80 kg) uses a 3.0-m-long rope to pull Bob (mass 60 kg) across the floor (?k = 0.20) at a constant speed of 1.0 m/s. Bob signals to Andy to stop by “plucking” the rope, sending a wave pulse forward along the rope. The pulse reaches Andy 150 ms later. What is the mass of the rope?

Problem 54GP If a bungee cord is stretched horizontally to a length of 2.5 m, the tension in the cord is 2.1 N. A transverse pulse on the cord travels from one end to the other in 0.80 s. If the cord is stretched to a length of 3.5 m, the pulse takes the same time of 0.80 s to travel from one end to the other. What is the tension in the cord when it is stretched to this length?

Problem 56GP In 2003, an earthquake in Japan generated 1.1 Hz waves that traveled outward at 7.0 km/s. 200 km to the west, seismic instruments recorded a maximum acceleration of 0.25g along the east-west axis. a. How much time elapsed between the earthquake and the first detection of the waves? b. Was this a transverse or a longitudinal wave? c. What was the wavelength? d. What was the maximum horizontal displacement of the ground as the wave passed?

Problem 55GP Suing 1 in Figure 55 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? FIGURE 55

Problem 57GP A coyote can locate a sound source with good accuracy by comparing the arrival times of a sound wave at its two ears. Suppose a coyote is listening to a bird whistling at 1000 Hz. The bird is 3.0 m away, directly in front of the coyote’s right ear. The coyote’s ears are 15 cm apart. a. What is the difference in the arrival time of the sound at the left ear and the right ear? b. What is the ratio of this time difference to the period of the sound wave? 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?

Problem 58GP An earthquake produces longitudinal P waves that travel outward at 8000 m/s and transverse S waves that move at 4500 m/s. A seismograph at some distance from the earthquake records the arrival of the S waves 2.0 min after the arrival of the P waves. How far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Problem 59GP 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 4°C, the average sound speed is 1480 m/s. It’s known from laboratory measurements that the sound speed increases 4.0 m/s for every 1.0°C 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?

Problem 60GP Figure P15.62 shows two snapshot graphs taken 10 ms apart, with the blue curve being the first snapshot. What are the (a)wavelength, (b) speed, (c) frequency, and (d) amplitude of this wave?

Problem 61GP Low-frequency vertical oscillations are one possible cause of motion sickness, with 0.3 Hz having the strongest effect. Your boat is bobbing in place at just the right frequency to cause you the maximum discomfort. a. How much time elapses between two waves hitting the ship? ________________ b. If the wave crests appear to be about 30 m apart, what would you estimate to be the speed of me waves?

Problem 62GP A wave on a string is described by y (x, t) = (3.0 cm)× cos [2?(x/(2.4 m) + t/(0.20 s))], where x is in m and t in s. a. In what direction is this wave traveling? b. What are the wave speed, frequency, and wavelength? c. At t = 0.50 s, what is the displacement of the string at x = 0.20 m?

Problem 63GP Write the y-equation for a wave traveling in the negative x-direction with wavelength 50 cm, speed 4.0 m/s, and amplitude 5.0 cm.

Problem 64GP Write the y-equation for a wave traveling in the positive x-direction with frequency 200 Hz, speed 400 m/s, and amplitude 0.010 mm.

Problem 65GP A wave is described by the expression y(x, t) = (3.0 cm)× cos(1.5x ? 50t), where x is in m and t is in s. a. Draw an accurate snapshot graph of this wave. ________________ b. What is the speed of the wave and in what direction is it traveling?

Problem 66GP A point on a string undergoes simple harmonic motion as a sinusoidal wave passes. When a sinusoidal wave with speed 24 m/s, wavelength 30 cm, and amplitude of 1.0 cm passes, what is the maximum speed of a point on the string?

Problem 67GP A simple pendulum is made by attaching a small cup of sand with a hole in the bottom to a 1.2-m-long string. The pendulum is mounted on the back of a small motorized car. As the car drives forward, the pendulum swings from side to side and leaves a trail of sand as shown in Figure 67. How fast was the car moving? FIGURE 67

Problem 68GP a. A typical 100 W lightbulb produces 4.0 W of visible light. (The other 96 W are dissipated as heat and infrared radiation.) What is the light intensity on a wall 2.0 m away from the lightbulb? b. A krypton laser produces a cylindrical red laser beam 2.0 mm in diameter with 2.0 W of power. What is the light intensity on a wall 2.0 m away from the laser?

Problem 69GP 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.

Problem 70GP The earth’s average distance from the sun is 1.50 × 1011 m. At this distance, the intensity of radiation from the sun is 1.38 kW/m2. The earth’s radius is 6.37 × 106m. What is the total solar power received by the earth? (For comparison, total human power consumption is roughly 1013W

Problem 71GP Lasers can be used to drill or cut material. One such laser generates a series of high-intensity pulses rather than a continuous beam of light. Each pulse contains 500 mJ of energy and lasts 10 ns. The laser fires 10 such pulses per second. a. What is the peak power of the laser light? The peak power is the power output during one of the 10 ns pulses. ________________ b. What is the average power output of the laser? The average power is the total energy delivered per second. ________________ c. A lens focuses the laser beam to a 10-?m-diameter circle on the target. During a pulse, what is the light intensity on the target? ________________ d. The intensity of sunlight at the surface of the earth at midday is about 1100 W/m2. What is the ratio of the laser intensity on the target to the intensity of the midday sun?

Problem 72GP The quietest sound you can hear is 0 dB. Estimate the diameter of your ear canal and compute an approximate area. At 0 dB, how much sound power is “captured” by one ear? (Ignore any focusing of energy by the pinna, the external folds of your ear.)

Problem 73GP The sound intensity 50 m from a wailing tornado siren is 0.10 W/m2. a. What is the sound intensity level? ________________ b. In a noisy neighborhood, the weakest sound likely to be heard over background noise is 60 dB. Estimate the maximum distance at which the siren can be heard.

Problem 74GP A harvest mouse can detect sounds below the threshold of human hearing, as quiet as -10 dB. Suppose you are sitting in a field on a very quiet day while a harvest mouse sits nearby. A very gentle breeze causes a leaf 1.5 m from your head to rustle, generating a faint sound right at the limit of your ability to hear it. The sound of the rustling leaf is also right at the threshold of hearing of the harvest mouse. How far is the harvest mouse from the leaf?

Problem 75GP A speaker at an open-air concert emits 600 W of sound power, radiated equally in all directions. a. What is the intensity of the sound 5.0 m from the speaker? b. What sound intensity level would you experience there if you did not have any protection for your ears? c. Earplugs you can buy in the drugstore have a noise reduction rating of 23 decibels. If you are wearing those earplugs but your friend Phil is not, how far from the speaker should Phil stand to experience the same loudness as you?

Problem 77GP 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? Assume the room temperature is 20°C.

Problem 76GP A bat locates insects by emitting ultrasonic “chirps” and then listening for echoes. The lowest-frequency chirp of a big brown bat is 26 kHz. How fast would the bat have to fly, and hi what direction, for you to just barely be able to hear the chirp at 20 kHz?

Problem 78GP Ocean waves with wavelength 1.2 m and period 1.5 s are moving past a pier. A boy runs along the pier, in the direction opposite to the motion of the wave, at 3.5 m/s. How many wave crests pass the boy each second?

Problem 79GP A source of sound moves toward you at speed vs and away from Jane, who is standing on the other side of it. You hear the sound at twice the frequency as Jane. What is the speed of the source? Assume that the speed of sound is 340 m/s.

Problem 80GP When the heart pumps blood into the aorta, the pressure gradient—the difference between the blood pressure inside the heart and the blood pressure in the artery—is an important diagnostic measurement. A direct measurement of the pressure gradient is difficult, but an indirect determination can be made by inferring the pressure difference from a measurement of velocity. Blood is essentially at rest in the heart; when it leaves and enters the aorta, it speeds up significantly and—according to Bernoulli’s equation—the pressure must decrease. A doctor using 2.5 MHz ultrasound measures a 6000 Hz frequency shift as the ultrasound reflects from blood ejected from the heart. a. What is the speed of the blood in the aorta? b. What is the difference in blood pressure between the inside of the heart and the aorta? Assume that the patient is lying down and that there is no difference in height as the blood moves from the heart into the aorta.

Problem 81PP Echolocation As discussed in the chapter, many species of bats find flying insects by emitting pulses of ultrasound and listening for the reflections. This technique is called echolocation. Bats possess several adaptations that allow them to echolocate very effectively. Although we can’t hear them, the ultrasonic pulses are very loud. In order not to be deafened by the sound they emit, bats can temporarily turn off their hearing. Muscles in the ear cause the bones in their middle ear to separate slightly, so that they don’t transmit vibrations to the inner ear. After an ultrasound pulse ends, a bat can hear an echo from an object a minimum of 1 m away. Approximately how much time after a pulse is emitted is the bat ready to hear its echo? A. 0.5 ms B. 1 ms C. 3 ms D. 6 ms

Problem 82PP Echolocation As discussed in the chapter, many species of bats find flying insects by emitting pulses of ultrasound and listening for the reflections. This technique is called echolocation. Bats possess several adaptations that allow them to echolocate very effectively. Bats are sensitive to very small changes in frequency of the reflected waves. What information does this allow them to determine about their prey? A. Size B. Speed C. Distance D. Species

Problem 83PP As discussed in the chapter, many species of bats find flying insects by emitting pulses of ultrasound and listening for the reflections. This technique is called echolocation. Bats possess several adaptations that allow them to echolocate very effectively. Some bats have specially shaped noses that they use to focus the ultrasound pulses in the forward direction. Why is this useful? A. They are not distracted by echoes from several directions. B. The energy of the pulse is concentrated in a smaller area, so the intensity is larger. C. The pulse goes forward only, so it doesn’t affect the bat’s hearing.

Problem 84PP Echolocation As discussed in the chapter, many species of bats find flying insects by emitting pulses of ultrasound and listening for the reflections. This technique is called echolocation. Bats possess several adaptations that allow them to echolocate very effectively. Some bats utilize a sound pulse with a rapidly decreasing frequency. A decreasing-frequency pulse has A. Decreasing wavelength. B. Decreasing speed. C. Increasing wavelength. D. Increasing speed.