Question: Figure P13.74 shows a crude model

> A steel wire with mass 25.0 g and length 1.35 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m. (a) Compute the linear density of the string. (b) What velocity wave on the string will produce the desired fundamental frequen

> A distance of 5.00 cm is measured between two adjacent nodes of a standing wave on a 20.0 - cm - long string. (a) In which harmonic number n is the string vibrating? (b) Find the frequency of this harmonic if the string has a mass of 1.75 x 10–2 kg and a

> A stretched string of length L is observed to vibrate in five equal segments when driven by a 630.-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in three segments?

> How far, and in what direction, should a cellist move her finger to adjust a string’s tone from an out - of - tune 449 Hz to an in - tune 440 Hz? The string is 68.0 cm long, and the finger is 20.0 cm from the nut for the 449-Hz tone.

> A stretched string fixed at each end has a mass of 40.0 g and a length of 8.00 m. The tension in the string is 49.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (b) What is the vibration frequency for this harmonic?

> A steel wire in a piano has a length of 0.700 0 m and a mass of 4.300 x 10-3 kg. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle C (fC = 261.6 Hz on the chromatic musical scale)?

> A pair of speakers separated by a distance d = 0.700 m are driven by the same oscillator at a frequency of 686 Hz. An observer originally positioned at one of the speakers begins to walk along a line perpendicularto the line joining the speakers as in Fi

> Two loudspeakers are placed above and below each other, as in Figure P14.40 and driven by the same source at a frequency of 4.50 x 102 Hz. An observer is in front of the speakers (to the right) at point O, at the same distance from each speaker. What min

> Two small containers, each with a volume of 1.00 x 102 cm3, contain helium gas at 0°C and 1.00 atm pressure. The two containers are joined by a small open tube of negligible volume, allowing gas to flow from one container to the other. What common pressu

> A dolphin located in seawater at a temperature of 25°C emits a sound directed toward the bottom of the ocean 150 m below. How much time passes before it hears an echo?

> The ship in Figure P14.39 travels along a straight line parallel to the shore and a distance d = 600 m from it. The ship’s radio receives simultaneous signals of the same frequency from antennas A and B, separated b y a distance L = 800

> The acoustical system shown in Figure P14.38 is driven by a speaker emitting sound of frequency 756 Hz. (a) If constructive interference occurs at a particular instant, by what minimum amount should the path length in the upper U-shaped tube be increased

> Two cars are stuck in a traffic jam and each sounds its horn at a frequency of 625 Hz. A bicyclist between the two cars, 4.50 m from each horn (Fig. P14.37), is disturbed to find she is at a point of constructive interference. How far backward must she m

> A yellow submarine traveling horizontally at 11.0 m/s uses sonar with a frequency of 5.27 x 103 Hz. A red submarine is in front of the yellow submarine and moving 3.00 m/s relative to the water in the same direction. A crewman in the red submarine observ

> A supersonic jet traveling at Mach 3.00 at an altitude of h = 2.00 x 104 m is directly over a person at time t = 0 as shown in Figure P14.35. Assume the average speed of sound in air is 335 m/s over the path of the sound. (a) At what time will the person

> Expectant parents are thrilled to hear their unborn baby’s heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus’s ventricular wall moves in simple harmonic motion with amplitude 1.80 mm and frequency 115 beats per minute. The motion de

> A tuning fork vibrating at 512 Hz falls from rest and accelerates at 9.80 m/s2. How far below the point of release is the tuning fork when waves of frequency 485 Hz reach the release point?

> An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 465 Hz when the train is approaching him and 441 Hz when the train is receding from him. Using these frequencies, he calcu

> At rest, a car’s horn sounds the note A (440 Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one-third the car’s speed hears a frequency of 415 Hz. (a) Is the cyclist ahead of or behind the

> Following a collision in outer space, a copper disk at 850°C is rotating about its axis with an angular speed of 25.0 rad/s. As the disk radiates infrared light, its temperature falls to 20.0°C. No external torque acts on the disk. (a) Does the angular s

> On a hot summer day, the temperature of air in Arizona reaches 114°F. What is the speed of sound in air at this temperature?

> Two trains on separate tracks move toward each other. Train 1 has a speed of 1.30 x 102 km/h; train 2, a speed of 90.0 km/h. Train 2 blows its horn, emitting a frequency of 5.00 x 102 Hz. What is the frequency heard by the engineer on train 1?

> An airplane traveling at half the speed of sound emits a sound of frequency 5.00 kHz. At what frequency does a stationary listener hear the sound (a) As the plane approaches? (b) After it passes?

> A commuter train passes a passenger platform at a constant speed of 40.0 m/s. The train horn is sounded at its characteristic frequency of 320. Hz. (a) What overall change in frequency is detected by a person on the platform as the train moves from appro

> A train is moving past a crossing where cars are waiting for it to pass. While waiting, the driver of the lead car becomes sleepy and rests his head on the steering wheel, unintentionally activating the car’s horn. A passenger in the back of the train he

> A baseball hits a car, breaking its window and triggering its alarm which sounds at a frequency of 1250 Hz. What frequency is heard by a boy on a bicycle riding away from the car at 6.50 m/s?

> A skyrocket explodes 100 m above the ground (Fig. P14.24). Three observers are spaced 100 m apart, with the first (A) directly under the explosion. (a) What is the ratio of the sound intensity heard by observer A to that heard by observer B? (b) What is

> Show that the difference in decibel levels β1 and β 2 of a sound source is related to the ratio of its distances r1 and r2 from the receivers by the formula

> An outside loudspeaker (considered a small source) emits sound waves with a power output of 100 W. (a) Find the intensity 10.0 m from the source. (b) Find the intensity level in decibels at that distance. (c) At what distance would you experience the sou

> A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of 50. dB by an observer 10 km away. (a) What is the average power generated by the horn? (b) What intensity level of the horn’s sound is observed by someone

> A 250-m-long bridge is improperly designed so that it cannot expand with temperature. It is made of concrete with α = 12 x 10-6 (°C)-1. (a) Assuming the maximum change in temperature at the site is expected to be 20°C, find the change in length the span

> A family ice show is held at an enclosed arena. The skaters perform to music playing at a level of 80.0 dB. This intensity level is too loud for your baby, who yells at 75.0 dB. (a) What total sound intensity engulfs you? (b) What is the combined sound l

> Earthquakes at fault lines in Earth’s crust create seismic waves, which are longitudinal (P - waves) or transverse (S - waves). The P-waves have a speed of about 7 km/s. Estimate the average bulk modulus of Earth’s crust given that the density of rock is

> There is evidence that elephants communicate via in-frasound, generating rumbling vocalizations as low as 14 Hz that can travel up to 10.km. The intensity level of these sounds can reach 103 dB, measured a distance of 5.0 m from the source. Determine the

> A trumpet creates a sound intensity level of 1.15 X 102 dB at a distance of 1.00 m. (a) What is the sound intensity of a trumpet at this distance? (b) What is the sound intensity of five trumpets at this distance? (c) Find the sound intensity of five tru

> The toadfish makes use of resonance in a closed tube to produce very loud sounds. The tube is its swim bladder, used as an amplifier. The sound level of this creature has been measured as high as 100. dB. (a) Calculate the intensity of the sound wave emi

> The area of a typical eardrum is about 5.0 x 10-5 m2. Calculate the sound power (the energy per second) incident on an eardrum at (a) The threshold of hearing and (b) The threshold of pain.

> A person wears a hearing aid that uniformly increases the intensity level of all audible frequencies of sound by 30.0 dB. The hearing aid picks up sound having a frequency of 250 Hz at an intensity of 3.0 x 10-11 W/m2. What is the intensity delivered to

> A sound wave from a siren has an intensity of 100.0 W/m2 at a certain point, and a second sound wave from a nearby ambulance has an intensity level 10 dB greater than the siren’s sound wave at the same point. What is the intensity level of the sound wave

> One of the loudest sounds in recent history was that made by the explosion of Krakatoa on August 26–27, 1883. According to barometric measurements, the sound had a decibel level of 180 dB at a distance of 161 km. Assuming the intensity falls off as the i

> The intensity level produced by a jet airplane at a certain location is 150 dB. (a) Calculate the intensity of the sound wave generated by the jet at the given location. (b) Compare the answer to part (a) to the threshold of pain and explain why employee

> A bimetallic strip of length L is made of two ribbons of different metals bonded together. (a) First assume the strip is originally straight. As the strip is warmed, the metal with the greater average coefficient of expansion expands more than the other,

> The mating call of a male cicada is among the loudest noises in the insect world, reaching decibel levels of 105 dB at a distance of 1.00 m from the insect. (a) Calculate the corresponding sound intensity. (b) Calculate the sound intensity at a distance

> A person standing 1.00 m from a portable speaker hears its sound at an intensity of 7.50 x 10-3 W/m2. (a) Find the corresponding decibel level. (b) Find the sound intensity at a distance of 35.0 m, assuming the sound propagates as a spherical wave. (c) F

> Suppose you hear a clap of thunder 16.2 s after seeing the associated lightning stroke. The speed of light in air is 3.00 x 108 m/s. (a) How far are you from the lightning stroke? (b) Do you need to know the value of the speed of light to answer? Explain

> A slingshot consists of a light leather cup containing a stone. The cup is pulled back against two parallel rubber bands. It takes a force of 15.0 N to stretch either one of these bands 1.00 cm. (a) What is the potential energy stored in the two bands to

> A block of mass m = 2.00 kg is attached to a spring of force constant k = 5.00 x 102 N/m that lies on a horizontal frictionless surface as shown in Figure P13.8. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from

> A system consists of a vertical spring with force constant k = 1250 N/m, length L = 1.50 m, and object of mass m = 5.00 kg attached to the end (Fig. P13.76). The object is placed at the level of the point of attachment with the spring un-stretched, at po

> A 2.00 - kg block hangs without vibrating at the end of a spring (k = 500. N/m) that is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of g/3 when the acceleration suddenly ceases (at t = 0). (a) What is the ang

> Assume a hole is drilled through the center of the Earth. It can be shown that an object of mass m at a distance r from the center of the Earth is pulled toward the center only by the material in the shaded portion of Figure P13.73. Assume Earth has a un

> An object of mass m is connected to two rubber bands of length L, each under tension F, as in Figure P13.72. The object is displaced vertically by a small distance y. assuming the tension does not change, show that (a) The restoring force is -(2F/L)y and

> An expandable cylinder has its top connected to a spring with force constant 2.00 x 103 N/m (Fig. P10.64). The cylinder is filled with 5.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C. (a) If the lid

> A light balloon filled with helium of density 0.179 kg/ m3 is tied to a light string of length L = 3.00 m. The string is tied to the ground, forming an “inverted” simple pendulum (Fig. P13.71a). If the balloon is displ

> A spring in a toy gun has a spring constant of 9.80 N/m and can be compressed 20.0 cm beyond the equilibrium position. A 1.00 - g pellet resting against the spring is propelled forward when the spring is released. (a) Find the muzzle speed of the pellet.

> A spring 1.50 m long with force constant 475 N/m is hung from the ceiling of an elevator, and a block of mass 10.0 kg is attached to the bottom of the spring. (a) By how much is the spring stretched when the block is slowly lowered to its equilibrium poi

> A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.50 Hz. Block B rests on it, as shown in Figure P13.69, and the coefficient of static friction between the two is μs

> A 5.00 - g bullet moving with an initial speed of 400. m/s is fired into and passes through a 1.00 - kg block, as in Figure P13.68. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 900.

> A 3.00 - kg object is fastened to a light spring, with the intervening cord passing over a pulley (Fig. P13.67). The pulley is frictionless, and its inertia may be neglected. The object is released from rest when the spring is un-stretched. If the object

> A 0.500 - kg block is released from rest and slides down a frictionless track that begins 2.00 m above the horizontal, as shown in Figure P13.66. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring

> A simple pendulum has mass 1.20 kg and length 0.700 m. (a) What is the period of the pendulum near the surface of Earth? (b) If the same mass is attached to a spring, what spring constant would result in the period of motion found in part (a)?

> A certain tuning fork vibrates at a frequency of 196 Hz while each tip of its two prongs has an amplitude of 0.850 mm. (a) What is the period of this motion? (b) Find the wavelength of the sound produced by the vibrating fork, taking the speed of sound i

> An object of mass 2.00 kg is oscillating freely on a vertical spring with a period of 0.600 s. Another object of unknown mass on the same spring oscillates with a period of 1.05 s. Find (a) The spring constant k and (b) The unknown mass.

> Two concrete spans of a 250-m-long bridge are placed end to end so that no room is allowed for expansion (Fig. P10.63a). If the temperature increases by 20.0°C, what is the height y to which the spans rise when they buckle (Fig. P10.63b)? Fig

> The position of a 0.30 - kg object attached to a spring is described by x = (0.25 m) cos (0.4πt) Find (a) The amplitude of the motion, (b) The spring constant, (c) The position of the object at t = 0.30 s, and (d) The object’s speed at t = 0.30 s.

> A wave of amplitude 0.30 m interferes with a second wave of amplitude 0.20 m traveling in the same direction. What are (a) The largest and (b) The smallest resultant amplitudes that can occur, and under what conditions will these maxima and minima arise?

> A taut clothesline has length L and a mass M. A transverse pulse is produced by plucking one end of the clothesline. If the pulse makes n round trips along the clothesline in t seconds, find expressions for (a) The speed of the pulse in terms of n, L, an

> An archer must exert a force of 375 N on the bowstring shown in Figure P13.6a such that the string makes an angle of θ = 35.0° with the vertical. (a) Determine the tension in the bowstring. (b) If the applied force is replaced by

> A 2.65 - kg power line running between two towers has a length of 38.0 m and is under a tension of 12.5 N. (a) What is the speed of a transverse pulse set up on the line? (b) If the tension in the line was unknown, describe a procedure a worker on the gr

> The elastic limit of a piece of steel wire is 2.70 x 109 Pa. What is the maximum speed at which transverse wave pulses can propagate along the wire without exceeding its elastic limit? (The density of steel is 7.86 x 103 kg/m3.)

> Tension is maintained in a string as in Figure P13.57. The observed wave speed is v = 24.0 m/s when the suspended mass is m = 3.00 kg. (a) What is the mass per unit length of the string? (b) What is the wave speed when the suspended mass is m = 2.00 kg?

> A string is 50.0 cm long and has a mass of 3.00 g. A wave travels at 5.00 m/s along this string. A second string has the same length, but half the mass of the first. If the two strings are under the same tension, what is the speed of a wave along the sec

> A simple pendulum consists of a ball of mass 5.00 kg hanging from a uniform string of mass 0.060 0 kg and length L. If the period of oscillation of the pendulum is 2.00 s, determine the speed of a transverse wave in the string when the pendulum hangs ver

> An astronaut on the Moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large object suspended from it. Assume a wire of mass 4.00 g is 1.60 m long and has a 3.00 - kg object suspended from it. A pulse requires 3

> Before beginning a long trip on a hot day, a driver inflates an automobile tire to a gauge pressure of 1.80 atm at 300. K. At the end of the trip, the gauge pressure has increased to 2.20 atm. (a) Assuming the volume has remained constant, what is the te

> Transverse waves with a speed of 50.0 m/s are to be produced on a stretched string. A 5.00 - m length of string with a total mass of 0.060 0 kg is used. (a) What is the required tension in the string? (b) Calculate the wave speed in the string if the ten

> A student taking a quiz finds on a reference sheet the two equations f = 1/t and v = √T/μ She has forgotten what T represents in each equation. (a) Use dimensional analysis to determine the units required for T in each equation. (b) Explain how you can i

> A piano string of mass per unit length 5.00 x 10-3 kg/m is under a tension of 1350 N. Find the speed with which a wave travels on this string.

> Workers attach a 25.0 - kg mass to one end of a 20.0 - m long cable and secure the other end to the top of a stationary crane, suspending the mass in midair. If the cable has a mass of 12.0 kg, determine the speed of transverse waves at (a) The middle an

> A biologist hangs a sample of mass 0.725 kg on a pair of identical, vertical springs in parallel and slowly lowers the sample to equilibrium, stretching the springs by 0.200 m. Calculate the value of the spring constant of one of the springs.

> An ethernet cable is 4.00 m long and has a mass of 0.200 kg. A transverse wave pulse is produced by plucking one end of the taut cable. The pulse makes four trips down and back along the cable in 0.800 s. What is the tension in the cable?

> Ocean waves are traveling to the east at 4.0 m/s with a distance of 20.0 m between crests. With what frequency do the waves hit the front of a boat (a) When the boat is at anchor and (b) When the boat is moving westward at 1.0 m/s?

> Orchestra instruments are commonly tuned to match an A-note played by the principal oboe. The Baltimore Symphony Orchestra tunes to an A-note at 440 Hz while the Boston Symphony Orchestra tunes to 442 Hz. If the speed of sound is constant at 343 m/s, fin

> A bat can detect small objects, such as an insect, whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a frequency of 60.0 x 103 Hz and the speed of sound in air is 343 m/s, what is the smallest insect

> A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?

> A liquid with a coefficient of volume expansion of β just fills a spherical flask of volume V0 at temperature Ti (Fig. P10.61). The flask is made of a material that has a coefficient of linear expansion of a. The liquid is free to expand into

> The distance between two successive minima of a transverse wave is 2.76 m. Five crests of the wave pass a given point along the direction of travel every 14.0 s. Find (a) The frequency of the wave and (b) The wave speed.

> Light waves are electromagnetic waves that travel at 3.00 x 108 m/s. The eye is most sensitive to light having a wavelength of 5.50 x 10-7 m. Find (a) The frequency of this light wave and (b) Its period.

> An object attached to a spring vibrates with simple harmonic motion as described by Figure P13.42. For this motion, find (a) The amplitude, (b) The period, (c) The angular frequency, (d) The maximum speed, (e) The maximum acceleration, and (f) An equatio

> The sinusoidal wave shown in Figure P13.41 is traveling in the positive x - direction and has a frequency of 18.0 Hz. Find the (a) Amplitude, (b) Wavelength, (c) Period, and (d) Speed of the wave. Figure P13.41:

> A simple pendulum is 5.00 m long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What

> A spring is hung from a ceiling, and an object attached to its lower end stretches the spring by a distance d = 5.00 cm from its un-stretched position when the system is in equilibrium as in Figure P13.4. If the spring constant is 47.5 N/m, determine the

> The free - fall acceleration on Mars is 3.7 m/s2. (a) What length of pendulum has a period of 1.0 s on Earth? (b) What length of pendulum would have a 1.0 - s period on Mars? An object is suspended from a spring with force constant 10.0 N/m. Find the mas

> A coat hanger of mass m = 0.238 kg oscillates on a peg as a physical pendulum as shown in Figure P13.38. The distance from the pivot to the center of mass of the coat hanger is d = 18.0 cm and the period of the motion is T = 1.25 s. Find the moment of in

> A clock is constructed so that it keeps perfect time when its simple pendulum has a period of 1.000 s at locations where g = 9.800 m/s2. The pendulum bob has length L = 0.2482 m, and instead of keeping perfect time, the clock runs slow by 1.500 minutes p

> A “seconds” pendulum is one that moves through its equilibrium position once each second. (The period of the pendulum is 2.000 s.) The length of a second’s pendulum is 0.9927 m at Tokyo and 0.9942 m at Cambridge, England. What is the ratio of the free -

> A 20.0-L tank of carbon dioxide gas (CO2) is at a pressure of 9.50 x 105 Pa and temperature of 19.0°C. (a) Calculate the temperature of the gas in Kelvin. (b) Use the ideal gas law to calculate the number of moles of gas in the tank. (c) Use the periodic

> A simple pendulum has a length of 52.0 cm and makes 82.0 complete oscillations in 2.00 min. Find (a) The period of the pendulum and (b) The value of g at the location of the pendulum.

> A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 15.5 s. (a) How tall is the tower? (b) If this pendulum is taken to the Moon, where the free - fall a

> Given that x = A cos (ωt) is a sinusoidal function of time, show that v (velocity) and a (acceleration) are also sinusoidal functions of time.

> A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500 - kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the or