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physics
oscillations mechanical waves

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

Apiece of steel string is under tension. (a) If the tension doubles, the transverse wave speed (1) doubles, (2) halves, (3) increases by √2, (4) decreases by √2. Why? (b) If the linear mass density of a 10.0-m length of string is and it is under a tension of 9.00 N, what is the transverse
On a violin, a correctly tuned A string has a frequency of 440 Hz. If an A string produces sound at 450 Hz under a tension of 500 N, what should the tension be to produce the correct frequency?
Will a standing wave be formed in a 4.0-m length of stretched string that transmits waves at a speed of if it is driven at a frequency of (a) 15 Hz or (b) 20 Hz?
Two waves of equal amplitude and frequency of 250 Hz travel in opposite directions at a speed of 150 m/s in a string. If the string is 0.90 m long, for which harmonic mode is the standing wave set up in the string?
An object of mass 1.0 kg is attached to a spring with spring constant 15 N/m. If the object has a maximum speed of 0.50 m/s, what is the amplitude of oscillation?
A university physics professor buys 100 m of string and determines its total mass to be 0.150 kg. This string is used to set up a standing wave laboratory demonstration between two posts 3.0 m apart. If the desired second harmonic frequency is 35 Hz, what should be the required string tension?
String A has twice the tension but half the linear mass density as string B, and both strings have the same length. (a) The frequency of the first harmonic on string A is (1) four times, (2) twice, (3) half, (4) ¼ times that of string B. Explain. (b) If the lengths of the strings are 2.5 m and
You are setting up two standing string waves. You have a length of uniform piano wire that is 3.0 m long and has a mass of 0.150 kg. You cut this into two lengths, one of 1.0 m and the other of 2.0 m, and place each length under tension. What should be the ratio of tensions (expressed as short to
A violin string is tuned to a certain frequency (first harmonic or the fundamental frequency). (a) If a violinist wants a higher frequency, should the string be (1) lengthened, (2) kept the same length, or (3) shortened? Why? (b) If the string is tuned to 520 Hz and the violinist puts a finger
A tight uniform string with a length of 1.80 m is tied down at both ends and placed under a tension of 100 N. When it vibrates in its third harmonic (draw a sketch), the sound given off has a frequency of 75.0 Hz. What is the mass of the string?
In a common laboratory experiment on standing waves, the waves are produced in a stretched string by an electrical vibrator that oscillates at 60 Hz (Fig. 13.28). The string runs over a pulley, and a hanger is suspended from the end. The tension in the string is varied by adding weights to the
A student uses a 2.00-m-long steel string with a diameter of 0.90 mm for a standing wave experiment. The tension on the string is tweaked so that the second harmonic of this string vibrates at 25.0 Hz. (a) Calculate the tension the string is under. (b) Calculate the first harmonic frequency for
To study the effects of acceleration on the period of oscillation, a student puts a grandfather clock with a 0.9929-m-long pendulum inside an elevator. Find the period of the grandfather clock (a) When the elevator is stationary, (b) When the elevator is accelerating upward at 1.50 m/s2, (c)
A 0.500-kg mass is attached to a vertical spring and the system is allowed to come to equilibrium. The mass is then given an initial downward speed of 1.50 m/s. The mass travels downward 25.3 cm before stopping and returning. (a) Determine the spring constant. (b) What is its speed after it falls
During an earthquake, a house plant of mass 15.0 kg in a tall building oscillates with a horizontal amplitude of 10.0 cm at 0.50 Hz. What are the magnitudes of (a) The maximum velocity, (b) The maximum acceleration, and (c) The maximum force on the plant? (Assume SHM.)
Atoms in a solid are in continuous vibrational motion due to thermal energy. At room temperature, the amplitude of these atomic vibrations is typically about 10-9, and their frequency is on the order of 1012 Hz. (a) What is the approximate period of oscillation of a typical atom? (b) What is the
A 2.0-kg mass resting on a horizontal frictionless surface is connected to a fixed spring. The mass is displaced 16 cm from its equilibrium position and released. At t = 0.50s, the mass is 8.0 cm from its equilibrium position (and has not passed through it yet). (a) What is the period of
A simple pendulum is set into small-angle motion, making a maximum angle with the vertical of 5o. Its period is 2.21 s. (a) Determine its length. (b) Determine its maximum speed. (c) What is the acceleration of the pendulum bob when it is at the lowest position?
Spring A (50.0 N/m) is attached to the ceiling. The top of spring B (30.0 N/m)is hooked onto the bottom of spring A. Then a 0.250-kg mass is then attached to the bottom of Spring B. (a) How far will the object fall until it reaches equilibrium? (b) What is the period of the resulting oscillation?
A particle of mass 0.10 kg is attached to a spring of spring constant 10 N/m. If the maximum acceleration of the particle is 5.0 m/s2, what is the maximum speed of the particle?
(a) Is there a Doppler effect if a sound source and an observer are moving with the same velocity? (b) What would be the effect if a moving source accelerated toward a stationary observer?
(a) Why does it seem particularly quiet after a snowfall? (b) Why do empty rooms sound hollow? (c) Why do people’s voices sound fuller or richer when they sing in the shower?
The frets on a guitar finger board are spaced closer together the farther they are from the neck. Why is this? What would be the result if they were evenly spaced?
Is it possible for an open organ pipe and a closed organ pipe, each of the same length, to produce notes of the same frequency? Justify your answer.
How would an increase in air temperature affect the frequencies of an organ pipe?
When you blow across the mouth of an empty soda bottle, a particular tone is produced. If the bottle is filled to one-third its height with water, how would the tone be affected? Explain. How about if it were filled to one-half? (Consider only standing waves in the bottle.)*
A crystal wine glass is partially filled with water. A person wets her finger and rubs it around the rim of the glass, which produces sound. Why is this?
The speed of sound in air depends on temperature. What effect, if any, should humidity have?
What is the difference between sound intensity and sound intensity level?
Where is the intensity greater and by what factor: (1) at a point a distance R from a power source P, or (2) at a point a distance 2R from a power source of 2P? Explain.
The Richter scale, used to measure the intensity level of earthquakes, is a logarithmic scale, as is the decibel scale. Why are such logarithmic scales used?
What is the speed of sound in air at (a) 10oC and (b) 20oC?
Brass is an alloy of copper and zinc. Does the addition of zinc to copper cause an increase or decrease in the speed of sound in brass rods compared to copper? Explain.
The speed of sound in steel is about 4.50 km/s. A steel rail is struck with a hammer, and an observer 0.400 km away has one ear to the rail. (a) How much time will elapse from the time the sound is heard through the rail until the time it is heard through the air? Assume that the air temperature
A person holds a rifle horizontally and fires at a target. The bullet has a muzzle speed of 200 m/s, and the person hears the bullet strike the target 1.00 s after firing it. The air temperature is 72 oF. What is the distance to the target?
A freshwater dolphin sends an ultrasonic sound to locate a prey. If the echo off the prey is received by the dolphin 0.12 s after being sent, how far is the prey from the dolphin?
A submarine on the ocean surface receives a sonar echo indicating an underwater object. The echo comes back at an angle of above the horizontal and the echo took 2.32 s to get back to the submarine. What is the object’s depth?
The speed of sound in human tissue is on the order of 1500 m/s. A3.50-MHz probe is used for an ultrasonic procedure. (a) If the effective physical depth of the ultra-sound is 250 wavelengths, what is the physical depth in meters? (b) What is the time lapse for the ultrasound to make a round trip
The size of your eardrum (the tympanum; see Fig. 1 in Insight 14.2, The Physiology and Physics of the Ear and Hearing) partially determines the upper frequency limit of your audible region, usually between 16 000 Hz and 20 000 Hz. If the wavelength is on the order of twice the diameter of the
On hiking up a mountain that has several over-hanging cliffs, a climber drops a stone at the first cliff to determine its height by measuring the time it takes to hear the stone hit the ground. (a) At a second cliff that is twice the height of the first, the measured time of the sound from the
A bat moving at 15.0 m/s emits a high-frequency sound as it approaches a wall that is 25.0 m away. Assuming that the bat continues straight toward the wall, how far away is it when it receives the echo? (Assume the air temperature in the cave to be 0 º C.)
Sound propagating through air 30 oC at passes through a vertical cold front into air that is 4.0 oC. If the sound has a frequency of 2500 Hz, by what percentage does its wavelength change in crossing the boundary?
The speed of sound in air on a summer day is 350 m/s. What is the air temperature?
Calculate the intensity generated by a 1.0-W point source of sound at a location (a) 3.0 m and (b) 6.0 m from it.
(a) If the distance from a point sound source triples, the sound intensity will be (1) 3, (2) 1/3, (3) 9, (4) 1/9 times the original value. Why? (b) By how much must the distance from a point source be increased to reduce the sound intensity by half?
Assuming that the diameter of your eardrum is 1 cm (see Exercise 16), what is the sound power received by the eardrum at the threshold of (a) Hearing and (b) Pain?
A middle C note (262 Hz) is sounded on a piano to help tune a violin string. When the string is sounded, nine beats are heard in 3.0 s. (a) How much is the violin string off tune? (b) Should the string be tightened or loosened to sound middle C?
Calculate the intensity level for (a) The threshold of hearing and (b) The threshold of pain.
Find the intensity levels in decibels for sounds with intensities of (a) 10-2 W/m2, (b) 10-6 W/m2, and (c) 10-15 W/m2.
At Cape Canaveral, on blastoff a rocket produces an intensity level of 160 dB as measured 10 m from the rocket. What would be the intensity level at 100 m away? (Assume no energy is lost due to reflections, etc.)
(a) If the power of a sound source doubles, the intensity level at a certain distance from the source (1) increases, (2) exactly doubles, or (3) decreases. Why? (b) What are the intensity levels at a distance of 10 m from a 5.0-W and a 10-W source, respectively?
The intensity levels of two people holding a conversation are 60 dB and 70 dB, respectively. What is the intensity of the combined sounds?
A point source emits radiation in all directions at a rate of 7.5 kW. What is the intensity of the radiation 5.0 m from the source?
Sonar is used to map the ocean floor. If an ultrasonic signal is received 2.0 s after it is emitted, how deep is the ocean floor at that location?
Two sound sources have intensities of and 10-6 W/m2, respectively. Which source is more intense and by how many times more?
Average speech has an intensity level of about 60 dB. Assuming that 20 people all speak at 60 dB, what is the total sound intensity?
A rock band (with loud speakers) has an average intensity level of 110 dB at a distance of 15 m from the band. Assuming the sound is radiated equally over a hemisphere in front of the band, what is the total power output?
A person has a hearing loss of 30 dB for a particular frequency. What is the sound intensity that is heard at this frequency that has an intensity of the threshold of pain?
Noise levels for some common aircraft are given in Table 14.4. What are the lowest and highest intensities for(a) Takeoff and (b) Landing for these planes?
If the distance to a sound source is halved, (a) Will the sound intensity level change by a factor of (1) 2, (2) 1/2, (3) 4, (4) 1/4, or (5) none of the preceding? Why? (b) What is the change in the sound intensity level?
A compact speaker puts out 100 W of sound power. (a) Neglecting losses to the air, at what distance would the sound intensity be at the pain threshold? (b) Neglecting losses to the air, at what distance would the sound intensity be that of normal speech? Does your answer seem reasonable? Explain.
What is the intensity level of a 23-dB sound after being amplified (a) Ten thousand times, (b) A million times, (c) A billion times?
In a neighborhood challenge to see who can climb a tree the fastest, you are ready to climb. Your friends have surrounded you in a circle as a cheering section; each individual alone would cause a sound intensity level of 80 dB at your location. If the actual sound level at your location is 87 dB,
A dog’s bark has a sound intensity level of 40 dB. (a) If two of the same dogs were barking, the intensity level is (1) less than 40 dB, (2) between 40 dB and 80 dB, (3) 80 dB. (b) What would be the intensity level?
What temperature change from 0oC would increase the speed of sound by 1.0%?
At a rock concert, the average sound intensity level for a person in a front-row seat is 110 dB for a single band. If all the bands scheduled to play produce sound of that same intensity, how many of them would have to play simultaneously for the sound level to be at or above the threshold of pain?
At a distance of 12.0 m from a point source, the intensity level is measured to be 70 dB. At what distance from the source will the intensity level be 40 dB?
At a Fourth of July celebration, a firecracker explodes (Fig. 14.20). Considering the firecracker to be a point source, what are the intensities heard by observers at points B, C, and D, relative to that heard by the observer at A?
An office in an e-commerce company has fifty computers, which generate a sound intensity level of 40 dB (from the keyboards). The office manager tries to cut the noise to half as loud by removing twenty-five computers. Does he achieve his goal? What is the intensity level generated by twenty-five
A 1000-Hz tone from a loudspeaker has an intensity level of 100 dB at a distance of 2.5 m. If the speaker is assumed to be a point source, how far from the speaker will the sound have intensity levels (a) Of 60 dB and (b) Barely high enough to be heard?
During practice in a huddle, a quarterback shouts the play in anticipation of crowd noise during the actual game. To a receiver 0.750 m away from the quarterback in the huddle, it seems as loud as the noise from a screaming child. When they get into practice formation, the quarterback yells at
A bee produces a buzzing sound that is barely audible to a person 3.0 m away. How many bees would have to be buzzing at that distance to produce a sound with an intensity level of 50 dB?
A violinist and a pianist simultaneously sound notes with frequencies of 436 Hz and 440 Hz, respectively. What beat frequency will the musicians hear?
A violinist tuning her instrument to a piano note of 264 Hz detects three beats per second. (a) The frequency of the violin could be (1) less than 264 Hz, (2) equal to 264 Hz, (3) greater than 264 Hz, (4) both (1) and (3). Why? (b) What are the possible frequencies of the violin tone?
What is the frequency heard by a person driving directly toward a factory whistle (f = 800Hz) if the air temperature is 0oC?
The wave speed in a liquid is given by v = √B/p, where B is the bulk modulus of the liquid and is its density. Show that this equation is dimensionally correct. What about v = √Y/pfor a solid? (Y is Young’s modulus.)
On a day with a temperature of and no wind blowing, the frequency heard by a moving person from a 500-Hz stationary siren is 520 Hz. (a) The person is (1) moving toward, (2) moving away from, or (3) stationary relative to the siren. Explain. (b) What is the person’s speed?
While standing near a railroad crossing, you hear a train horn. The frequency emitted by the horn is 400 Hz. If the train is traveling at and the air temperature is 25 oC, what is the frequency you hear (a) When the train is approaching and (b) After it has passed?
Two identical strings on different cellos are tuned to the 440-Hz A note. The peg holding one of the strings slips, so its tension is decreased by 1.5%. What is the beat frequency heard when the strings are then played together?
How fast, in kilometers per hour, must a sound source be moving toward you to make the observed frequency greater than the true frequency? (Assume that the speed of sound is 340 m/s.)
You are driving east at 25.0 m/s as you notice an ambulance traveling west toward you at 35.0 m/s. The sound you detect from the sirens has a frequency of 300 Hz. (a) Is the true frequency of the sirens (1) greater than 300 Hz, (2) less than 300 Hz, or (3) exactly 300 Hz? (b) Determine the true
The frequency of an ambulance siren is 700 Hz. What are the frequencies heard by a stationary pedestrian as the ambulance approaches and moves away from her at a speed of 90.0 km/h? (Assume that the air temperature is 20 oC.)
A jet flies at a speed of Mach 2.0. What is the half-angle of the conical shock wave formed by the aircraft? Can you tell the speed of the shock wave?
A fighter jet flies at a speed of Mach 1.5. (a) If the jet were to fly faster than Mach 1.5, the half-angle of the conical shock wave would (1) increase, (2) remain the same, (3) decrease. Why? (b) What is the half-angle of the conical shock wave formed by the jet plane at Mach 1.5?
The half-angle of the conical shock wave formed by a supersonic jet is 30o. What are (a) The Mach number of the aircraft and (b) The actual speed of the aircraft if the air temperature is – 20 oC?
An observer is traveling between two identical sources of sound (frequency 100 Hz). His speed is 10.0 m/s as he approaches one and recedes from the other. (a) What frequency tone does he hear from each source? (b) How many beats per second does he hear? Assume normal room temperature.
A 0.75-m-long metal rod is dropped vertically onto a marble floor. When the rod strikes the floor, it is deter-mined electronically that the impact produces a 4-kHz tone. What is the speed of sound in the rod?
A bystander hears a siren vary in frequency from 476 Hz to 404 Hz as a fire truck approaches, passes by, and moves away on a straight street (Fig. 14.21). What is the speed of the truck? (Take the speed of sound in air to be 343 m/s.)
Bats emit sounds of frequencies around 35.0 kHz and use echolocation to find their prey. If a bat is moving with a speed of toward a hovering, stationary insect, (a) What is the frequency received by the insect if the air temperature is 20 oC? (b) What frequency of the reflected sound is heard by
A supersonic jet flies directly overhead relative to an observer, at an altitude of 2.0 km (Fig. 14.22). When the observer hears the first sonic boom, the plane has flown a horizontal distance of 2.5 km at a constant speed.(a) What is the angle of the shock wave cone? (b) At what Mach number is
The first three natural frequencies of an organ pipe are 126 Hz, 378 Hz, and 630 Hz. (a) Is the pipe an open or a closed pipe? (b) Taking the speed of sound in air to be 340 m/s, find the length of the pipe.
A closed organ pipe has a fundamental frequency of 528 Hz (a C note) at 20 oC. What is the fundamental frequency of the pipe when the temperature is 0 o?
The human ear canal is about 2.5 cm long. It is open at one end and closed at the other. (a) What is the fundamental frequency of the ear canal at 20 oC? (b) To what frequency is the ear most sensitive? (c) If a person’s ear canal is longer than 2.5 cm, is the fundamental frequency higher or
An organ pipe that is closed at one end has a length of 0.80 m. At 20 oC, what is the distance between a node and an adjacent antinode for (a) The second harmonic and (b) The third harmonic?
An open organ pipe and an organ pipe that is closed at one end both have lengths of 0.52 m at 20 oC. What is the fundamental frequency of each pipe?
An open organ pipe is 0.50 m long. If the speed of sound is 340 m/s, what are the pipe’s fundamental frequency and the frequencies of the first two overtones?
An organ pipe that is closed at one end is 1.10 m long. It is oriented vertically and filled with carbon dioxide gas (which is denser than air and thus will stay in the pipe). A tuning fork with a frequency of 60.0 Hz can be used to set up a standing wave in the fundamental mode. What is the speed
A tuning fork vibrates at a frequency of 256 Hz. (a) When the air temperature increases, the wavelength of the sound from the tuning fork (1) increases, (2) remains the same, (3) decreases. Why? (b) If the temperature rises from 0 oC to 20 oC, what is the change in the wavelength?
An open organ pipe 0.750 m long has its first over-tone at a frequency of 441 Hz. What is the temperature of the air in the pipe?
When all of its holes are closed, a flute is essentially a tube that is open at both ends, with the length measured from the mouthpiece to the far end (as in Fig. 14.16b). If a hole is open, then the length of the tube is effectively measured from the mouthpiece to the hole. (a) Is the position at

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