College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 14, Problem 81AP
To determine
The required tension in the rod.
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By proper excitation, it is possible to produce both longitudinal and transverse waves in a long metal rod. In a particular case, the rod is 150 cm long and 0.200 cm in radius and has a mass of 50.9 g. Young’s modulus for the material is 6.80 × 1010 Pa. Determine the required tension in the rod so that the ratio of the speed of longitudinal waves to the speed of transverse waves is 8.
The speed of sound in a solid medium is given by v = √E/p where E is the value of Young's modulus for the solid and p is the density. A sound
wave travels at 5.8 x 10³ m/s in a steel rod of length 1.02 m, diameter 2.0 cm and mass 7.0 kg. Use the data to determine the value of the Young's
modulus for steel. Give your answer in giga-pascal (GPa, 10⁹ Nm ²).
A metal bar with a length of 1.80 m has a density of 6200 kg/m3. Longitudinal sound waves travel from one end of the bar to the other in a time interval of 4.50×10−4 s. What is Young's modulus for this metal?
Express your answer in pascals.
Chapter 14 Solutions
College Physics
Ch. 14.3 - Which of the following actions will increase the...Ch. 14.6 - Suppose youre on a hot air balloon ride, carrying...Ch. 14.6 - As an airplane flying with constant velocity moves...Ch. 14.8 - Which of the following frequencies are higher...Ch. 14.10 - Prob. 14.5QQCh. 14.10 - Prob. 14.6QQCh. 14.11 - You are tuning a guitar by comparing the sound of...Ch. 14 - (a) You are driving down the highway in your car...Ch. 14 - When dealing with sound intensities and decibel...Ch. 14 - Fill in the blanks with the correct values (to two...
Ch. 14 - Explain how the distance to a lightning bolt (Fig....Ch. 14 - Two cars are on the same straight road. Car A...Ch. 14 - Why does a vibrating guitar string sound louder...Ch. 14 - You are driving toward the base of a cliff and you...Ch. 14 - Prob. 8CQCh. 14 - Prob. 9CQCh. 14 - Prob. 10CQCh. 14 - An airplane mechanic notices that the sound from a...Ch. 14 - Suppose you hear a clap of thunder 16.2 s after...Ch. 14 - Earthquakes at fault lines in Earths crust create...Ch. 14 - On a hot summer day, the temperature of air in...Ch. 14 - A dolphin located in seawater at a temperature of...Ch. 14 - A group of hikers hears an echo 3.00 s after...Ch. 14 - The range of human hearing extends from...Ch. 14 - Prob. 7PCh. 14 - A stone is dropped from rest into a well. The...Ch. 14 - A hammer strikes one end of a thick steel rail of...Ch. 14 - A person standing 1.00 m from a portable speaker...Ch. 14 - The mating call of a male cicada is among the...Ch. 14 - The intensity level produced by a jet airplane at...Ch. 14 - One of the loudest sounds in recent history was...Ch. 14 - A sound wave from a siren has an intensity of...Ch. 14 - A person wears a hearing aid that uniformly...Ch. 14 - The area of a typical eardrum is about 5.0 105...Ch. 14 - The toadfish makes use of resonance in a closed...Ch. 14 - A trumpet creates a sound intensity level of 1.15 ...Ch. 14 - There is evidence that elephants communicate via...Ch. 14 - A family ice show is held at an enclosed arena....Ch. 14 - A train sounds its horn as it approaches an...Ch. 14 - An outside loudspeaker (considered a small source)...Ch. 14 - Show that the difference in decibel levels 1 and 2...Ch. 14 - A skyrocket explodes 100 m above the ground (Fig....Ch. 14 - The Doppler Effect A baseball hits a car, breaking...Ch. 14 - A train is moving past a crossing where cars are...Ch. 14 - A commuter train passes a passenger platform at a...Ch. 14 - An airplane traveling at half the speed of sound...Ch. 14 - Two trains on separate tracks move toward each...Ch. 14 - At rest, a cars horn sounds the note A (440 Hz)....Ch. 14 - An alert physics student stands beside the tracks...Ch. 14 - A bat flying at 5.00 m/s is chasing an insect...Ch. 14 - A tuning fork vibrating at 512 Hz falls from rest...Ch. 14 - Expectant parents are thrilled to hear their...Ch. 14 - A supersonic jet traveling at Mach 3.00 at an...Ch. 14 - A yellow submarine traveling horizontally at 11.0...Ch. 14 - Two cars are stuck in a traffic jam and each...Ch. 14 - The acoustical system shown in Figure P14.38 is...Ch. 14 - Prob. 39PCh. 14 - Prob. 40PCh. 14 - A pair of speakers separated by a distance d =...Ch. 14 - Prob. 42PCh. 14 - A stretched string fixed at each end has a mass of...Ch. 14 - Prob. 44PCh. 14 - A stretched string of length L is observed to...Ch. 14 - A distance of 5.00 cm is measured between two...Ch. 14 - A steel wire with mass 25.0 g and length 1.35 m is...Ch. 14 - Prob. 48PCh. 14 - A 12.0-kg object hangs in equilibrium from a...Ch. 14 - In the arrangement shown in Figure P14.50, an...Ch. 14 - Prob. 51PCh. 14 - Standing-ware vibrations are set up in a crystal...Ch. 14 - A cars 30.0-kg front tire is suspended by a spring...Ch. 14 - Prob. 54PCh. 14 - Prob. 55PCh. 14 - The overall length of a piccolo is 32.0 cm. The...Ch. 14 - The human ear canal is about 2.8 cm long. If it is...Ch. 14 - A tunnel under a river is 2.00 km long. (a) At...Ch. 14 - A pipe open at both ends has a fundamental...Ch. 14 - The adjacent natural frequencies of an organ pipe...Ch. 14 - A guitarist sounds a tuner at 196 Hz while his...Ch. 14 - Two nearby trumpets are sounded together and a...Ch. 14 - Prob. 63PCh. 14 - The G string on a violin has a fundamental...Ch. 14 - Two train whistles have identical frequencies of...Ch. 14 - Two pipes of equal length are each open at one...Ch. 14 - A student holds a tuning dork oscillating at 256...Ch. 14 - Prob. 68PCh. 14 - Some studies suggest that the upper frequency...Ch. 14 - A typical sound level for a buzzing mosquito is 40...Ch. 14 - Assume a 150 W loudspeaker broadcasts sound...Ch. 14 - Two small loudspeakers emit sound waves of...Ch. 14 - An interstate highway has been built through a...Ch. 14 - Prob. 74APCh. 14 - Prob. 75APCh. 14 - Prob. 76APCh. 14 - On a workday, the average decibel level of a busy...Ch. 14 - Prob. 78APCh. 14 - A block with a speaker bolted to it is connected...Ch. 14 - A student stands several meters in front of a...Ch. 14 - Prob. 81APCh. 14 - A 0.500-m-long brass pipe open at both ends has a...
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- As shown in Figure P14.37, water is pumped into a tall, vertical cylinder at a volume flow rate R. The radius of the cylinder is r, and at the open top of the cylinder a tuning fork is vibrating with a frequency f. As the water rises, what time interval elapses between successive resonances? Figure P14.37 Problems 37 and 38.arrow_forwardThe bulk modulus of water is 2.2 109 Pa (Table 15.2). The density of water is 103 kg/m3 (Table 15.1). Find the speed of sound in water and compare your answer with the value given in Table 17.1.arrow_forwardAs in Figure P18.16, a simple harmonic oscillator is attached to a rope of linear mass density 5.4 102 kg/m, creating a standing transverse wave. There is a 3.6-kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 43.2 rad/s and an amplitude of 24.6 cm. a. What is the distance between adjacent nodes? b. If the angular frequency of the oscillator doubles, what happens to the distance between adjacent nodes? c. If the mass of the block is doubled instead, what happens to the distance between adjacent nodes? d. If the amplitude of the oscillator is doubled, what happens to the distance between adjacent nodes? FIGURE P18.16arrow_forward
- A sound wave in air has a pressure amplitude equal to 4.00 103 Pa. Calculate the displacement amplitude of the wave at a frequency of 10.0 kHz.arrow_forwardA string with a mass m = 8.00 g and a length L = 5.00 m has one end attached to a wall; the other end is draped over a small, fixed pulley a distance d = 4.00 m from the wall and attached to a hanging object with a mass M = 4.00 kg as in Figure P14.21. If the horizontal part of the string is plucked, what is the fundamental frequency of its vibration? Figure P14.21arrow_forwardReview. An aluminum wire is held between two clamps under zero tension at room temperature. Reducing the temperature, which results in a decrease in the wires equilibrium length, increases the tension in the wire. Taking the cross-sectional area of the wire to be 5.00 10-6 m2, the density to be 2.70 103 kg/m3, and Young's modulus to be 7.00 1010 N/m2, what strain (L/L.) results in a transverse wave speed of 100 m/s?arrow_forward
- Review. For the arrangement shown in Figure P14.60, the inclined plane and the small pulley are frictionless; the string supports the object of mass M at the bottom of the plane; and the string has mass m. The system is in equilibrium, and the vertical part of the string has a length h. We wish to study standing waves set up in the vertical section of the string. (a) What analysis model describes the object of mass M? (b) What analysis model describes the waves on the vertical part of the string? (c) Find the tension in the string. (d) Model the shape of the string as one leg and the hypotenuse of a right triangle. Find the whole length of the string. (e) Find the mass per unit length of the string. (f) Find the speed of waves on the string. (g) Find the lowest frequency for a standing wave on the vertical section of the string. (h) Evaluate this result for M = 1.50 kg, m = 0.750 g, h = 0.500 m, and θ = 30.0°. (i) Find the numerical value for the lowest frequency for a standing wave on the sloped section of the string. Figure P14.60arrow_forwardA ski gondola is connected to the top of a hill by a steel cable of length 660 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 17 s for the pulse to return. a) What is the speed of the pulse? b) What is the tension in the cable?arrow_forwardA copper wire has a density of ρ = 8920 kg/m3, a radius of 1.20 mm, and a length L. The wire is held under a tension of 10.00 N. Transverse waves are sent down the wire. (a) What is the linear mass density of the wire? (b) What is the speed of the waves through the wire?arrow_forward
- Problem 11: You decide to make one of the world’s largest musical instruments, using long cylindrical steel rods that are clamped tightly at both ends. The speed of longitudinal waves in rods of the type of steel you use is 5141 m/s and the steel has a Young’s modulus of 196 GPa. Part (a) What is the density of the steel, in kilograms per cubic meter? Part (b) When a longitudinal wave is excited in one of the steel rods in your instrument to produce resonance, will the rod’s ends be nodes or antinodes? Nodes ✔ Correct! Part (c) A standard frequency for tuning musical instruments is 440 Hz for the pitch of A above middle C, denoted A4. What is the length, in meters, of the steel rod that produces the pitch A4 as its fundamental longitudinal resonance? Part (d) Assume, instead, that you want to create a smaller version of this, using the same kind of construction, with one rod of length 13.5 cm. What would the fundamental longitudinal resonance frequency of that rod…arrow_forwardA copper wire, whose cross-sectional area is 8.58 x 106 m², has a linear density of 6.18 x 103 kg/m and is strung between two walls. At the ambient temperature, a transverse wave travels with a speed of 60.8 m/s on this wire. The coefficient of linear expansion for copper is 17 x 10-6 (Cº)-1, and Young's modulus for copper is 1.1 x 10¹1 N/m². What will be the speed of the wave when the temperature is lowered by 26.5 Cº? Ignore any change in the linear density caused by the change in temperature. Number i Unitsarrow_forwardA copper wire has a density of 8920 kg per cubic meter, a radius of 1.5mm and an unknown length. The wire is held under a tension of 12N. transverse waves are sent through the wire, (a) determine the linear density of the wire, (b) determine the speed through which wave travel through the wire.arrow_forward
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