Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 17, Problem 35PQ
To determine
Show that the kinetic energy in one wavelength of harmonic transverse wave on a rope.
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Two steel guitar strings have the same length.
String A has a diameter of 0.51 mm and is under
430.0 N of tension. String B has a diameter of 1.0
mm and is under a tension of 800.0 N . You may
want to review (Pages 461 - 463).
Part A
Find the ratio of the wave speeds, va/vB, in these two strings.
Express your answer using two significant figures.
nν ΑΣφ
va/vB =
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Consider a monochromatic green lightwave with wavelength λ = 550 nm (1 nm = 1 * 10-9m). Assuming the speed of light in vacuum (which is close to the one in air) to be c = 3 * 108m/s, then:
A. Calculate the period τ and the optical frequency v for green light?
B. Write a sinusoidal harmonic wave with unit amplitude propagating towards the negative x-axis. Consider that for x = 0 and t = 0, the (initial) phase is (π/2).
C. Plot the wave profile against x for following times: t = 0, 0.25τ, 0.5τ, and 0.75τ. Assume an arbitrary unit for the y-axis.
P13.34 Show that the following pairs of wave functions are
orthogonal over the indicated range.
a. e ax² and x(x² - 1)e-αx², -∞0 ≤ x <∞ where a is a
constant that is greater than zero
b. (6r/ao - r²/az)e-r/3ao and (r/ao)er/ao cos
interval 0 ≤r <∞0,0 ≤ 0 ≤ π,0 ≤ ≤ 2T
over the
Chapter 17 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 17.2 - As weve seen before, terms used in physics often...Ch. 17.2 - A graph of a pulses profile and a...Ch. 17.3 - Prob. 17.3CECh. 17.5 - Prob. 17.4CECh. 17.5 - The bulk modulus of water is 2.2 109 Pa (Table...Ch. 17.6 - Prob. 17.6CECh. 17 - A dog swims from one end of a pool to the opposite...Ch. 17 - Prob. 2PQCh. 17 - Prob. 3PQCh. 17 - Prob. 4PQ
Ch. 17 - Prob. 5PQCh. 17 - Prob. 6PQCh. 17 - Prob. 7PQCh. 17 - Prob. 8PQCh. 17 - A sinusoidal traveling wave is generated on a...Ch. 17 - Prob. 10PQCh. 17 - Prob. 11PQCh. 17 - The equation of a harmonic wave propagating along...Ch. 17 - Prob. 13PQCh. 17 - Prob. 14PQCh. 17 - Prob. 15PQCh. 17 - A harmonic transverse wave function is given by...Ch. 17 - Prob. 17PQCh. 17 - Prob. 18PQCh. 17 - Prob. 19PQCh. 17 - Prob. 20PQCh. 17 - Prob. 21PQCh. 17 - Prob. 22PQCh. 17 - A wave on a string with linear mass density 5.00 ...Ch. 17 - A traveling wave on a thin wire is given by the...Ch. 17 - Prob. 25PQCh. 17 - Prob. 26PQCh. 17 - Prob. 27PQCh. 17 - Prob. 28PQCh. 17 - Prob. 29PQCh. 17 - Prob. 30PQCh. 17 - Prob. 31PQCh. 17 - Problems 32 and 33 are paired. N Seismic waves...Ch. 17 - Prob. 33PQCh. 17 - Prob. 34PQCh. 17 - Prob. 35PQCh. 17 - Prob. 36PQCh. 17 - Prob. 37PQCh. 17 - Prob. 38PQCh. 17 - Prob. 39PQCh. 17 - Prob. 40PQCh. 17 - Prob. 41PQCh. 17 - Prob. 42PQCh. 17 - Prob. 43PQCh. 17 - Prob. 44PQCh. 17 - Prob. 45PQCh. 17 - What is the sound level of a sound wave with...Ch. 17 - Prob. 47PQCh. 17 - The speaker system at an open-air rock concert...Ch. 17 - Prob. 49PQCh. 17 - Prob. 50PQCh. 17 - Prob. 51PQCh. 17 - Prob. 52PQCh. 17 - Prob. 53PQCh. 17 - Using the concept of diffraction, discuss how the...Ch. 17 - Prob. 55PQCh. 17 - Prob. 56PQCh. 17 - An ambulance traveling eastbound at 140.0 km/h...Ch. 17 - Prob. 58PQCh. 17 - Prob. 59PQCh. 17 - Prob. 60PQCh. 17 - Prob. 61PQCh. 17 - In Problem 61, a. Sketch an image of the wave...Ch. 17 - Prob. 63PQCh. 17 - Prob. 64PQCh. 17 - Prob. 65PQCh. 17 - Prob. 66PQCh. 17 - Prob. 67PQCh. 17 - Prob. 68PQCh. 17 - Prob. 69PQCh. 17 - Prob. 70PQCh. 17 - A block of mass m = 5.00 kg is suspended from a...Ch. 17 - A The equation of a harmonic wave propagating...Ch. 17 - Prob. 73PQCh. 17 - Prob. 74PQCh. 17 - Prob. 75PQCh. 17 - Prob. 76PQCh. 17 - A siren emits a sound of frequency 1.44103 Hz when...Ch. 17 - Female Aedes aegypti mosquitoes emit a buzz at...Ch. 17 - A careless child accidentally drops a tuning fork...Ch. 17 - Prob. 80PQCh. 17 - A wire with a tapered cross-sectional area is...
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- A copper wire has a density of =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(a) At an air show a jet flies directly toward the stands at a speed of 1200 km/h, emitting a frequency of 3500 Hz, on a day when the speed of sound is 342 m/s. What frequency is received by the observers? (b) What frequency do they receive as the plane flies directly away from them?arrow_forward(a) What is the fundamental frequency of a 0.672-mlong tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?arrow_forward
- The equation of a harmonic wave propagating along a stretched string is represented by y(x, t) = 4.0 sin (1.5x 45t), where x and y are in meters and the time t is in seconds. a. In what direction is the wave propagating? be. N What are the b. amplitude, c. wavelength, d. frequency, and e. propagation speed of the wave?arrow_forwardA standing wave on a string is described by the equation y(x, t) = 1.25 sin(0.0350x) cos(1450t), where x is in centimeters, t is in seconds, and the resulting amplitude is in millimeters. a. What is the length of the string if this standing wave represents the first harmonic vibration of the string? b. What is the speed of the wave on this string?arrow_forward(a) What is the speed of sound in a medium where a 100-kHz frequency produces a 5.96-cm wavelength? (b) Which substance in Table 17.1 is this likely to be?arrow_forward
- A sinusoidal traveling wave is generated on a string by an oscillating source that completes 120 cycles per minute. What is the wavelength of the wave if individual crests are observed to travel 15.0 m in 1.00 min?arrow_forwardThe wave function for a standing wave on a 2.00-m-long string is given by y = 0.0500 sin(2x)cos(76t), where x and y are in meters and t is in seconds. a. How many antinodes are present? b. What is the fundamental frequency of this wave?arrow_forwardThe Channel Tunnel, or Chunnel, stretches 37.9 km undersea across the Strait of Dover in the English Channel between France and the United Kingdom. What are the resonant frequencies along this direction for the air in the Chunnel?arrow_forward
- A pulse moving along the x axis can be modeled as the wave function y(x,t)=4.00me( x+( 2.00m/s )t 1.00m)2 . (a)What are the direction and propagation speed of the pulse? (b) How far has the wave moved in 3.00 s? (c) Plot the pulse using a spreadsheet at time t=0.00 s and t=3.00 s to verify your answer in part (b).arrow_forward(a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is 18.0°C. (b) What is its fundamental frequency at 25.0°C?arrow_forwardA block of mass m = 5.00 kg is suspended from a wire that passes over a pulley and is attached to a wall (Fig. P17.71). Traveling waves are observed to have a speed of 33.0 m/s on the wire. a. What is the mass per unit length of the wire? b. What would the speed of waves on the wire be if the suspended mass were decreased to 2.50 kg? FIGURE P17.71arrow_forward
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Wave Speed on a String - Tension Force, Intensity, Power, Amplitude, Frequency - Inverse Square Law; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=vEzftaDL7fM;License: Standard YouTube License, CC-BY
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