Statistics For Business And Economics 12th Edition James T. McClave, P. George Benson, Terry T Sincich - Solutions

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Transverse pulses travel with a speed of 200 m/s along a taut copper wire whose diameter is 1.50 mm. What is the tension in the wire? (The density of copper is 8.92 g/cm3.)
Transverse waves travel with a speed of 20.0 m/s in a string under a tension of 6.00 N. What tension is required for a wave speed of 30.0 m/s in the same string?
A simple pendulum consists of a ball of mass M hanging from a uniform string of mass m and length L, with m
The elastic limit of the steel forming a piece of wire is equal to 2.70 X 108 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire without exceeding this stress? (The density of steel is 7.86 – 103 km/m3.)
A light string with a mass per unit length of 8.00 g/m has its ends tied to two walls separated by a distance equal to three fourths of the length of the string (Fig. P16.30)An object of mass m is suspended from the center of the string, putting a tension in the string.(a) Find an expression for
A 30.0-m steel wire and a 20.0-m copper wire both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. How long does it take a transverse wave to travel the entire length of the two wires?
A light string of mass m and length L has its ends tied to two walls that are separated by the distance D. Two objects, each of mass M, are suspended from the string as in Figure P16.32. If a wave pulse is sent from point A, how long does it take to travel to point B?
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) Identify the physical quantity each T
A taut rope has a mass of 0.180 kg and a length of 3.60 m. What power must be supplied to the rope in order to generate sinusoidal waves having amplitude of 0.100 m and a wavelength of 0.500 m and traveling with a speed of 30.0 m/s?
A two-dimensional water wave spreads in circular ripples. Show that the amplitude A at a distance r from the initial disturbance is proportional to 1 / r. (Suggestion: Consider the energy carried by one outward-moving ripple.)
Transverse waves are being generated on a rope under constant tension. By what factor is the required power increased or decreased if (a) The length of the rope is doubled and the angular frequency remains constant, (b) The amplitude is doubled and the angular frequency is halved, (c) Both
Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string that has a linear mass density of 4.00 - 10"2 kg/m. If the source can deliver a maximum power of 300W and the string is under a tension of 100 N, what is the highest frequency at which the source can operate?
It is found that a 6.00-m segment of a long string contains four complete waves and has a mass of 180 g. The string is vibrating sinusoidally with a frequency of 50.0 Hz and a peak-to-valley distance of 15.0 cm. (The “peak-to-valley” distance is the vertical distance from the farthest positive
A sinusoidal wave on a string is described by the equation y = (0.15 m) sin(0.80x ─ 50t) Where x and y are in meters and t is in seconds. If the mass per unit length of this string is 12.0 g/m, determine (a) The speed of the wave, (b) The wavelength, (c) The frequency, and (d) The
The wave function for a wave on a taut string is y(x, t) = (0.350 m) s in (10πt - 3πx + π/4) where x is in meters and t in seconds. (a) What is the average rate at which energy is transmitted along the string if the linear mass density is 75.0 g/m? (b) What is the energy
A horizontal string can transmit a maximum power PO (without breaking) if a wave with amplitude A and angular frequency ' is traveling along it. In order to increase this maximum power, a student folds the string and uses this “double string” as a medium. Determine the maximum power that can be
In a region far from the epicenter of an earthquake, a seismic wave can be modeled as transporting energy in a single direction without absorption, just as a string wave does. Suppose the seismic wave moves from granite into mudfill with similar density but with a much lower bulk modulus. Assume
(a) Evaluate A in the scalar equality (7 + 3) 4 = A. (b) Evaluate A, B, and C in the vector equality 7.00i + 3.00k = Ai + Bj + Ck. Explain how you arrive at the answers to convince a student who thinks that you cannot solve a single equation for three different unknowns. (c) What If? The
Show that the wave function y = eb(x─vt) is a solution of the linear wave equation (Eq. 16.27), where b is a constant.
Show that the wave function y = In [b(x ─vt)] is a solution to Equation 16.27, where b is a constant.
(a) Show that the function y(x, t) = x2 + v2t2 is a solution to the wave equation. (b) Show that the function in part (a) can be written as f (x # vt) # g(x " vt), and determine the functional forms for f and g. (c) What If? Repeat parts (a) and (b) for the function y(x, t) = sin (x) cos (vt).
€œThe wave€ is a particular type of pulse that can propagate through a large crowd gathered at a sports arena to watch a soccer or American football match (Figure P16.47). The elements of the medium are the spectators, with zero position corresponding to their being seated and
A traveling wave propagates according to the expression y = (4.0 cm) sin (2.0x ─ 3.0t), where x is in centimeters and t is in seconds. Determine (a) The amplitude, (b) The wavelength, (c) The frequency, (d) The period, and (e) The direction of travel of the wave. The wave function
The wave function for a traveling wave on a taut string is (in SI units) y(x, t) = (0.350 m) sin (10πt ─ 3πx + π/4) (a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.100 m? (c) What are
A transverse wave on a string is described by the equation y(x, t) = (0.350 m) sin (1.25 rad/m)x + (99.6 rad/s)t] Consider the element of the string at x ! 0. (a) What is the time interval between the first two instants when this element has a position of y = 0.175 m? (b) What distance does the
Motion picture film is projected at 24.0 frames per second. Each frame is a photograph 19.0 mm high. At what constant speed does the film pass into the projector?
A block of mass M, supported by a string, rests on an incline making an angle θ with the horizontal (Fig. P16.52). The length of the string is L, and its mass is m
A 2.00-kg block hangs from a rubber cord, being supported so that the cord is not stretched. The unstretched length of the cord is 0.500 m, and its mass is 5.00 g. The “spring constant” for the cord is 100 N/m. The block is released and stops at the lowest point. (a) Determine the tension in
A block of mass M hangs from a rubber cord. The block is supported so that the cord is not stretched. The unstretched length of the cord is L0 and its mass is m, much less than M. The “spring constant” for the cord is k. The block is released and stops at the lowest point. (a) Determine the
(a) Determine the speed of transverse waves on a string under a tension of 80.0 N if the string has a length of 2.00 m and a mass of 5.00 g. (b) Calculate the power required to generate these waves if they have a wavelength of 16.0 cm and amplitude of 4.00 cm.
A sinusoidal wave in a rope is described by the wave function y = (0.20 m) sin (0.75πx + 18πt) Where x and y are in meters and t is in seconds. The rope has a linear mass density of 0.250 kg/m. If the tension in the rope is provided by an arrangement like the one illustrated in Figure
A block of mass 0.450 kg is attached to one end of a cord of mass 0.003 20 kg; the other end of the cord is attached to a fixed point. The block rotates with constant angular speed in a circle on a horizontal frictionless table. Through what angle does the block rotate in the time that a transverse
A wire of density 0 is tapered so that its cross-sectional area varies with x according to A = (1.0 X 10─3 x + 0.010) cm2 (a) If the wire is subject to a tension T, derive a relationship for the speed of a wave as a function of position. (b) What If? If the wire is aluminum and is
A rope of total mass m and length L is suspended vertically. Show that a transverse pulse travels the length of the rope in a time interval Δt = 2√Lig. (Suggestion: First find an expression for the wave speed at any point a distance x from the lower end by considering the tension in the
If an object of mass M is suspended from the bottom of the rope in Problem 59, (a) Show that the time interval for a transverse pulse to travel the length of the rope is Δt = 2 √L/ mg (√M + m ─√M) What If? (b) Show that this reduces to the result of Problem 59
It is stated in Problem 59 that a pulse travels from the bottom to the top of a hanging rope of length L in a time interval Δt = 2√L/g. Use this result to answer the following questions. (It is not necessary to set up any new integration.) (a) How long does it take for a pulse to travel
Determine the speed and direction of propagation of each of the following sinusoidal waves, assuming that x and y are measured in meters and t in seconds (a) y = 0.60 cos(3.0x ─ 15t + 2) (b) y = 0.40 cos(3.0x + 15t ─ 2) (c) y = 1.2 sin(15t + 2.0x) (d) y = 0.20 sin[12t ─ (x/2)
An aluminum wire is clamped at each end under zero tension at room temperature. The tension in the wire is increased by reducing the temperature, which results in a decrease in the wire’s equilibrium length. What strain (ΔL/L) results in a transverse wave speed of 100 m/s? Take the
If a loop of chain is spun at high speed, it can roll along the ground like a circular hoop without slipping or collapsing. Consider a chain of uniform linear mass density μ whose center of mass travels to the right at a high speed v0. (a) Determine the tension in the chain in terms of
(a) Show that the speed of longitudinal waves along a spring of force constant k is v = √kL/μ, where L is the unstretched length of the spring and + is the mass per unit length. (b) A spring with a mass of 0.400 kg has an unstretched length of 2.00 m and a force constant of 100 N/m.
A string of length L consists of two sections. The left half has mass per unit length μ = μ0/2, while the right has a mass per unit length μ = 3μ = 3μ0/2. Tension in the string is T0. Notice from the data given that this string has the same total mass as a uniform string of
A pulse traveling along a string of linear mass density μ is described by the wave function y = [A0e─bx] sin (kx ─ wt) Where the factor in brackets before the sine function is said to be the amplitude (a) What is the power P (x) carried by this wave at a point x? (b) What is
An earthquake on the ocean floor in the Gulf of Alaska produces a tsunami (sometimes incorrectly called a “tidal wave”) that reaches Hilo, Hawaii, 4 450 km away, in a time interval of 9 h 30 min. Tsunamis have enormous wavelengths (100 to 200 km), and the propagation speed for these waves is v
A string on a musical instrument is held under tension T and extends from the point x = 0 to the point x = L. The string is over wound with wire in such a way that its mass per unit length μ(x) increases uniformly from + 0 at x = 0 to μL at x = L. (a) Find an expression for μ(x) as
Suppose that you hear a clap of thunder 16.2 s after seeing the associated lightning stroke. The speed of sound waves in air is 343 m/s, and the speed of light is 3.00 X 108 m/s. How far are you from the lightning stroke?
Find the speed of sound in mercury, which has a bulk modulus of approximately 2.80 X 1010 N/m2 and a density of 13 600 kg/m3.
A flowerpot is knocked off a balcony 20.0 m above the sidewalk and falls toward an unsuspecting 1.75-m-tall man who is standing below. How close to the sidewalk can the flower pot fall before it is too late for a warning shouted from the balcony to reach the man in time? Assume that the man below
The speed of sound in air (in m/s) depends on temperature according to the approximate expression v = 331.5 + 0.607TC where TC is the Celsius temperature. In dry air the temperature decreases about 1°C for every 150 m rise in altitude. (a) Assuming this change is constant up to an altitude of 9
A cowboy stands on horizontal ground between two parallel vertical cliffs. He is not midway between the cliffs. He fires a shot and hears its echoes. The second echo arrives 1.92 s after the first and 1.47 s before the third. Consider only the sound traveling parallel to the ground and reflecting
A rescue plane flies horizontally at a constant speed searching for a disabled boat. When the plane is directly above the boat, the boat’s crew blows a loud horn. By the time the plane’s sound detector perceives the horn’s sound, the plane has traveled a distance equal to half its altitude
A bat (Fig P17.7) can detect very small objects, such as an insect whose length is approximately equal to one wavelength of the sound the bat makes. If a bat emits chirps at a frequency of 60.0 kHz, and if the speed of sound in air is 340 m/s, what is the smallest insect the bat can detect?
An ultrasonic tape measure uses frequencies above 20 MHz to determine dimensions of structures such as buildings. It does this by emitting a pulse of ultrasound into air and then measuring the time for an echo to return from a reflecting surface whose distance away is to be measured. The distance
Ultrasound is used in medicine both for diagnostic imaging and for therapy. For diagnosis, short pulses of ultrasound are passed through the patient’s body. An echo reflected from a structure of interest is recorded, and from the time delay for the return of the echo the distance to the structure
A sound wave in air has a pressure amplitude equal to 4.00 x 10-3 N/m2. Calculate the displacement amplitude of the wave at a frequency of 10.0 kHz.
A sinusoidal sound wave is described by the displacement wave function s(x, t) = (2.00 μm) cos[(15.7 m-1)x - (858 s-1)t] (a) Find the amplitude, wavelength, and speed of this wave. (b) Determine the instantaneous displacement from equilibrium of the elements of air at the position x =
As a certain sound wave travels through the air, it produces pressure variations (above and below atmospheric pressure) given by ΔP = 1.27 sin (πx ─ 340πt) in SI units. Find (a) The amplitude of the pressure variations, (b) The frequency, (c) The wavelength in air, and
Write an expression that describes the pressure variation as a function of position and time for a sinusoidal sound wave in air, if A # 0.100 m and ΔPmax = 0.200 N/m2.
Write the function that describes the displacement wave corresponding to the pressure wave in Problem 13.
An experimenter wishes to generate in air a sound wave that has displacement amplitude of 5.50 X 10─6 m. The pressure amplitude is to be limited to 0.840 N/m2. What is the minimum wavelength the sound wave can have?
The tensile stress in a thick copper bar is 99.5% of its elastic breaking point of 13.0 X 1010 N/m2. If a 500-Hz sound wave is transmitted through the material, (a) What displacement amplitude will cause the bar to break? (b) What is the maximum speed of the elements of copper at this moment?
Prove that sound waves propagate with a speed given by Equation 17.1. Proceed as follows. In Figure 17.3, consider a thin cylindrical layer of air in the cylinder with face area A and thickness Δx. Draw a free-body diagram of this thin layer. Show that ∑Fx = max implies that ─
The area of a typical eardrum is about 5.00 X 10─5 m2. Calculate the sound power incident on an eardrum at (a) the threshold of hearing and (b) The threshold of pain.
Calculate the sound level in decibels of a sound wave that has an intensity of 4.00 "W/m2.
A vacuum cleaner produces sound with a measured sound level of 70.0 dB. (a) What is the intensity of this sound in W/m2? (b) What is the pressure amplitude of the sound?
The intensity of a sound wave at a fixed distance from a speaker vibrating at 1.00 kHz is 0.600 W/m2. (a) Determine the intensity if the frequency is increased to 2.50 kHz while a constant displacement amplitude is maintained. (b) Calculate the intensity if the frequency is reduced to 0.500 kHz
The intensity of a sound wave at a fixed distance from a speaker vibrating at a frequency f is I. (a) Determine the intensity if the frequency is increased to f while constant displacement amplitude is maintained. (b) Calculate the intensity if the frequency is reduced to f/2 and the displacement
The most soaring vocal melody is in Johann Sebastian Bach’s Mass in B minor. A portion of the score for the Credo section, number 9, bars 25 to 33, appears in Figure P17.23. The repeating syllable O in the phrase “resurrection moratorium” (the resurrection of the dead) is seamlessly passed
The tube depicted in Figure 17.2 is filled with air at 20°C and equilibrium pressure 1 atm. The diameter of the tube is 8.00 cm. The piston is driven at a frequency of 600 Hz with an amplitude of 0.120 cm. What power must be supplied to maintain the oscillation of the piston?
A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 dB. This 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 level?
Consider sinusoidal sound waves propagating in these three different media: air at 0°C, water, and iron. Use densities and speeds from Tables 14.1 and 17.1. Each wave has the same intensity I0 and the same angular frequency wo. (a) Compare the values of the wavelength in the three media. (b)
The power output of a certain public address speaker is 6.00 W. Suppose it broadcasts equally in all directions. (a) Within what distance from the speaker would the sound be painful to the ear? (b) At what distance from the speaker would the sound be barely audible?
Show that the difference between decibel levels B1 and B2 of a sound is related to the ratio of the distances r1 and r2 from the sound source by B2 ─ B2 = 20 log (r1/r2)
A firework charge is detonated many meters above the ground. At a distance of 400 m from the explosion, the acoustic pressure reaches a maximum of 10.0 N/m2. Assume that the speed of sound is constant at 343 m/s throughout the atmosphere over the region considered, that the ground absorbs all the
A loudspeaker is placed between two observers who are 110 m apart, along the line connecting them. If one observer records a sound level of 60.0 dB and the other records a sound level of 80.0 dB, how far is the speaker from each observer?
Two small speakers emit sound waves of different frequencies. Speaker A has an output of 1.00 mW, and speaker B has an output of 1.50 mW. Determine the sound level (in dB) at point C (Fig. P17.31) if (a) only speaker A emits sound, (b) only speaker B emits sound, and (c) both speakers emit sound.
A jackhammer, operated continuously at a construction site, behaves as a point source of spherical sound waves. A construction supervisor stands 50.0 m due north of this sound source and begins to walk due west. How far does she have to walk in order for the amplitude of the wave function to drop
The sound level at a distance of 3.00 m from a source is 120 dB. At what distance will the sound level be (a) 100 dB and (b) 10.0 dB?
A fireworks rocket explodes at a height of 100 m above the ground. An observer on the ground directly under the explosion experiences an average sound intensity of 7.00 X 10─2 W/m2 for 0.200 s. (a) What is the total sound energy of the explosion? (b) What is the sound level in decibels
As the people sing in church, the sound level everywhere inside is 101 dB. No sound is transmitted through the massive walls, but all the windows and doors are open on a summer morning. Their total area is 22.0 m2. (a) How much sound energy is radiated in 20.0 min? (b) Suppose the ground is a
The smallest change in sound level that a person can distinguish is approximately 1 dB. When you are standing next to your power lawnmower as it is running, can you hear the steady roar of your neighbor’s lawnmower? Perform an order-of-magnitude calculation to substantiate your answer, stating
A train is moving parallel to a highway with a constant speed of 20.0 m/s. A car is traveling in the same direction as the train with a speed of 40.0 m/s. The car horn sounds at a frequency of 510 Hz, and the train whistle sounds at a frequency of 320 Hz. (a) When the car is behind the train,
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 of 1.80 mm and a frequency of 115 per minute. (a) Find the maximum linear speed of the heart
Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 480 Hz. Determine the ambulances speed from these observations.
A block with a speaker bolted to it is connected to a spring having spring constant k = 20.0 N/m as in Figure P17.40. The total mass of the block and speaker is 5.00 kg, and the amplitude of this unit€™s motion is 0.500 m.(a) If the speaker emits sound waves of frequency 440 Hz, determine
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? Take the speed of sound in air to be 340 m/s.
At the Winter Olympics, an athlete rides her luge down the track while a bell just above the wall of the chute rings continuously. When her sled passes the bell, she hears the frequency of the bell fall by the musical interval called a minor third. That is, the frequency she hears drops to five
A siren mounted on the roof of a firehouse emits sound at a frequency of 900 Hz. A steady wind is blowing with a speed of 15.0 m/s. Taking the speed of sound in calm air to be 343 m/s, find the wavelength of the sound (a) Upwind of the siren and (b) Downwind of the siren. Firefighters are
The Concorde can fly at Mach 1.50, which means the speed of the plane is 1.50 times the speed of sound in air. What is the angle between the direction of propagation of the shock wave and the direction of the plane’s velocity?
When high-energy charged particles move through a transparent medium with a speed greater than the speed of light in that medium, a shock wave, or bow wave, of light is produced. This phenomenon is called the Cerenkov effect. When a nuclear reactor is shielded by a large pool of water, Cerenkov
The loop of a circus ringmaster’s whip travels at Mach 1.38 (that is, vS/v = 1.38). What angle does the shock wave make with the direction of the whip’s motion?
A supersonic jet traveling at Mach 3.00 at an altitude of 20 000 m is directly over a person at time t = 0 as in Figure P17.47.(a) How long will it be before the person encounters the shock wave?(b) Where will the plane be when it is finally heard? (Assume the speed of sound in air is 335 m/s.)
This problem represents a possible (but not recommended) way to code instantaneous pressures in a sound wave into 16-bit digital words. Example 17.2 mentions that the pressure amplitude of a 120-dB sound is 28.7 N/m2. Let this pressure variation be represented by the digital code 65 536. Let zero
Only two recording channels are required to give the illusion of sound coming from any point located between two speakers of a stereophonic sound system. If the same signal is recorded in both channels, a listener will hear it coming from a single direction halfway between the two speakers. This
Assume that a loudspeaker broadcasts sound equally in all directions and produces sound with a level of 103 dB at a distance of 1.60 m from its center. (a) Find its sound power output. (b) If the salesperson claims to be giving you 150 W per channel, he is referring to the electrical power input
A large set of unoccupied football bleachers has solid seats and risers. You stand on the field in front of the bleachers and fire a starter’s pistol or sharply clap two wooden boards together once. The sound pulse you produce has no definite frequency and no wavelength. The sound you hear
Many artists sing very high notes in ad lib ornaments and cadenzas. The highest note written for a singer in a published score was F-sharp above high C, 1.480 kHz, for Zerbinetta in the original version of Richard Strauss’s opera Ariadne auf Naxos. (a) Find the wavelength of this sound in air.
A sound wave in a cylinder is described by Equations 17.2 through 17.4. Show that ΔP = ± pvw √s2max ─s2.
On a Saturday morning, pickup trucks and sport utility vehicles carrying garbage to the town dump form a nearly steady procession on a country road, all traveling at 19.7 m/s. From one direction, two trucks arrive at the dump every 3 min. A bicyclist is also traveling toward the dump, at 4.47 m/s.
The ocean floor is underlain by a layer of basalt that constitutes the crust, or uppermost layer, of the Earth in that region. Below this crust is found denser periodotite rock, which forms the Earth’s mantle. The boundary between these two layers is called the Mohorovicic discontinuity
For a certain type of steel, stress is always proportional to strain with Young’s modulus as shown in Table 12.1. The steel has the density listed for iron in Table 14.1. It will fail by bending permanently if subjected to compressive stress greater than its yield strength σy = 400 MPa. A

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Statistics For Business And Economics 12th Edition James T. McClave, P. George Benson, Terry T Sincich - Solutions

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