Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 16, Problem 4Q
To determine
To rank:
The waves according to their:
a) Wavelengths.
b) Speeds.
c) Angular frequencies (greatest first).
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y!
72 Two sinusoidal 120 Hz
waves, of the same frequency
and amplitude, are to be sent in
the positive direction of an x axis
that is directed along a cord un-
der tension. The waves can be
10
20
sent in phase, or they can be
phase-shifted. Figure 16-47
shows the amplitude y' of the re-
sulting wave versus the distance of the shift (how far one wave is
shifted from the other wave). The scale of the vertical axis is set
by y', = 6.0 mm. If the equations for the two waves are of the
form y(x, t) = ym sin(kx + wt), what are (a) ym, (b) k, (c) w, and
(d) the correct choice of sign in front of w?
Shift distance (cm)
Figure 16-47 Problem 72.
(uu)
2 In Fig. 16-24, wave 1 consists of a rectangular peak of height 4 units
and width d, and a rectangular valley of depth 2 units and width d. The
wave travels rightward along an x axis Choices 2, 3, and 4 are similar
waves, with the same heights, depths, and widths, that will travel leftward
along that axis and through wave 1. Right-going wave 1 and one of the
left-going waves will interfere as they pass through each other. With
which left-going wave will the interference give, for an instant, (a) the
deepest valley, (b) a flat line, and (c) a flat peak 2d wide?
(1)
(2)
(3)
(4)
GO Figure 16-46 shows
transverse acceleration a, versus
time t of the point on a string at
70
x = 0, as a wave in the form of
y(x, t) = ym sin (kx – wt + 4)
passes through that point. The
scale of the vertical axis is set
%3D
by a, = 400 m/s². What is ?
Figure 16-46 Problem 70.
(Caution: A calculator does not
always give the proper inverse trig function, so check your answer by
substituting it and an assumed value of w into y(x, t) and then plotting
the function.)
Chapter 16 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 16 - Prob. 1QCh. 16 - Prob. 2QCh. 16 - Prob. 3QCh. 16 - Prob. 4QCh. 16 - Prob. 5QCh. 16 - The amplitudes and phase differences for four...Ch. 16 - Prob. 7QCh. 16 - a If a standing wave on a siring is given by y't =...Ch. 16 - Prob. 9QCh. 16 - If you set up the seventh harmonic on a string, a...
Ch. 16 - Prob. 11QCh. 16 - If a wave yx, t = 6.0mm sinkx 600 rad/st ...Ch. 16 - Prob. 2PCh. 16 - A wave has an angular frequency of 110 rad/s and a...Ch. 16 - Prob. 4PCh. 16 - A sinusoidal wave travels along a string. The time...Ch. 16 - Prob. 6PCh. 16 - A transverse sinusoidal wave is moving along a...Ch. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - The equation of a transverse wave traveling along...Ch. 16 - Prob. 11PCh. 16 - GO The function yx, t = 15.0 cm cosx 15 t, with x...Ch. 16 - Prob. 13PCh. 16 - The equation of a transverse wave on a string is y...Ch. 16 - Prob. 15PCh. 16 - The speed of a transverse wave on a string is 170...Ch. 16 - The linear density of a string is 1.6 104 kg/m. A...Ch. 16 - Prob. 18PCh. 16 - SSM What is the speed of a transverse wave in a...Ch. 16 - The tension in a wire clamped at both ends is...Ch. 16 - ILW A 100 g wire is held under a tension of 250 N...Ch. 16 - A sinusoidal wave is traveling on a string with...Ch. 16 - SSM ILW A sinusoidal transverse wave is traveling...Ch. 16 - Prob. 24PCh. 16 - A uniform rope of mass m and length L hangs from a...Ch. 16 - A string along which waves can travel is 2.70 m...Ch. 16 - Prob. 27PCh. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Prob. 31PCh. 16 - What phase difference between two identical...Ch. 16 - Prob. 33PCh. 16 - Prob. 34PCh. 16 - SSM Two sinusoidal waves of the same frequency...Ch. 16 - Four waves are to be sent along the same string,...Ch. 16 - GO These two waves travel along the same string:...Ch. 16 - Two sinusoidal waves of the same frequency are to...Ch. 16 - Two sinusoidal waves of the same period, with...Ch. 16 - Two sinusoidal waves with identical wavelengths...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - SSM WWW What are a the lowest frequency, b the...Ch. 16 - A 125 cm length of string has mass 2.00 g and...Ch. 16 - Prob. 45PCh. 16 - String A is stretched between two clamps separated...Ch. 16 - Prob. 47PCh. 16 - If a transmission line in a cold climate collects...Ch. 16 - Prob. 49PCh. 16 - Prob. 50PCh. 16 - Prob. 51PCh. 16 - A rope, under a tension of 200 N and fixed at both...Ch. 16 - Prob. 53PCh. 16 - Prob. 54PCh. 16 - GO The following two waves are sent in opposite...Ch. 16 - A standing wave pattern on a string is described...Ch. 16 - A generator at one end of a very long string...Ch. 16 - GO In Fig. 16-42, a string, tied to a sinusoidal...Ch. 16 - GO In Fig. 16-43, an aluminum wire, of length L1 =...Ch. 16 - Prob. 60PCh. 16 - Prob. 61PCh. 16 - Prob. 62PCh. 16 - A wave has a speed of 240 m/s and a wavelength of...Ch. 16 - The equation of a transverse wave traveling alone...Ch. 16 - The equation of a transverse wave traveling along...Ch. 16 - Prob. 66PCh. 16 - Prob. 67PCh. 16 - Prob. 68PCh. 16 - Prob. 69PCh. 16 - Prob. 70PCh. 16 - A transverse sinusoidal wave is generated at one...Ch. 16 - Prob. 72PCh. 16 - Prob. 73PCh. 16 - Prob. 74PCh. 16 - a What is the fastest transverse wave that can be...Ch. 16 - A standing wave results from the sum of two...Ch. 16 - Prob. 77PCh. 16 - Prob. 78PCh. 16 - Prob. 79PCh. 16 - When played in a certain manner, the lowest...Ch. 16 - A sinusoidal transverse wave traveling in the...Ch. 16 - Two sinusoidal waves of the same wavelength travel...Ch. 16 - Prob. 83PCh. 16 - Prob. 84PCh. 16 - Prob. 85PCh. 16 - a Write an equation describing a sinusoidal...Ch. 16 - A wave on a string is described by yx, t = 15.0...Ch. 16 - Prob. 88PCh. 16 - Two waves are described by...Ch. 16 - Prob. 90PCh. 16 - SSM In a demonstration, a 1.2 kg horizontal rope...Ch. 16 - Prob. 92PCh. 16 - A traveling wave on a string is described by...Ch. 16 - Prob. 94PCh. 16 - Prob. 95PCh. 16 - Consider a loop in the standing wave created by...
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- 66 Figure 16-44 shows the dis- placement y versus time t of the point on a string at x= 0, as a wave passes through that point. The scale of the y axis is set by y, = 6.0 mm. The wave is given by y(x, t) = ym sin(kx – wt + 4). What is 4? (Caution: A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of w into y(x, 1) and then plotting the function.) y (mm) Figure 16-44 Problem 66.arrow_forwardFigure 17-37 shows a transmitter and receiver of waves con- tained in a single instrument. It is used to measure the speed u of a target object (idealized as a flat plate) that is moving directly toward the unit, by analyzing the waves reflected from the target. What is u if the emitted frequency is 18.0 kHz and the detected frequency (of the returning waves) is 22.2 kHz?arrow_forwardA transverse wave traveling along an x axis has the fornm given by (16-18) y =y," sin(kx ± ω1 + φ). Figure 16-8a gives the displacement of string elements as a function of , al at time0. Figure 16-8h gives the displacements of the element at x 0 as a function oft. Find the values of the quantities shown in Eq. 16-18, including the correct choice of sign. (min) 10 20 -10 -20 -9 *レ b)arrow_forward
- 106 Figure 17-50 shows a transmitter and receiver of waves con- tained in a single instrument. It is used to measure the speed u of a target object (idealized as a flat plate) that is moving directly to- ward the unit, by analyzing the waves reflected from the target. What is u if the emitted frequency is 18.0 kHz and the detected fre- quency (of the returning waves) is 22.2 kHz? Target Figure 17-50 Problem 106.arrow_forwardIn Fig. 16-42, a string, tied to a sinusoidal oscillator at Pand running over a support at Q, is stretched by a block of mass m.The separation L between P and Q is 1.20 m, and the frequency fof the oscillator is fixed at 120 Hz.The amplitude of the motion atP is small enough for that point to be considered a node.A nodealso exists at Q. A standing wave appears when the mass of thehanging block is 286.1 g or 447.0 g, but not for any intermediatemass.What is the linear density of the string?arrow_forwardReference: Problem 11-93. A bat emits an ultrasound burst (frequency = f) as it flies toward a cave wall at speed v. At what frequency does the bat perceive the reflected pulse? Assume air at 20 °C. f = 50.6 kHz; v = 7.7 m/s]arrow_forward
- 93. ssm Suppose that the linear density of the A string on a violin is 7.8 x 10-4 kg/m. A wave on the string has a frequency of 440 Hz and a wavelength of 65 cm. What is the tension in the string?arrow_forward27P. A sinusoidal transverse wave is traveling along a string toward decreasing x. Figure 17-29 shows a plot of the displace- ment as a function of position at time t= 3.6 N, and its linear density is 25 g/m. Find (a) the amplitude, (b) 0. The string tension is the wavelength, (c) the wave speed, and (d) the period of the wave. (e) Find the maximum speed of a particle in the string. (f) Write an equation describing the traveling wave. 6. 4 2. -2 -4 -6 10 20 30 40 50 60 70 80 x (cm) FIGURE 17-29 Problem 27.arrow_forward-8 O Figure 16-32 shows the trans- verse velocity u versus time t of the point on a string at x = 0, as a wave passes through it. The scale on the ver- tical axis is set by u, = 4.0 m/s. The inkr - uf - d What thes is e (Caution: A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of o into y(x, 1) and then plotting the function.) Figure 16-32 Problem 8.arrow_forward
- 2 In Fig. 17-25, two point sources S. S, and S2, which are in phase, emit identical sound waves of wave- S,. length 2.0 m. In terms of wave- lengths, what is the phase differ- ence between the waves arriving at point P if (a) L1 = 38 m and L2 = 34 m, and (b) L, = 39 m and L2 = 36 m? (c) Assuming that the source separation is much smaller than L1 and L2, what type of interference occurs at P in situations (a) and (b)? Figure 17-25 Question 2.arrow_forward95 A continuous traveling wave with amplitude A is incident on a boundary. The continuous reflection, with a smaller amplitude B, travels back through the incoming wave. The resulting interference pattern is displayed in Fig. 16-51. The standing wave ratio is defined to be A + B А — В SWR The reflection coefficient R is the ratio of the power of the reflected wave to the Ana Amin Am max ах power of the incoming wave and is thus proportional to the ratio (BIA). What is the SWR for (a) total reflection and (b) no reflection? (c) For SWR = 1.50, what is R expressed as a percentage? Figure 16-51 Problem 95.arrow_forward95 A continuous traveling wave with amplitude A is incident on a boundary. The continuous reflection, with a smaller amplitude B, travels back through the incoming wave. The resulting interference pattern is displayed in Fig. 16-51. The standing wave ratio is defined to be A + B А - В SWR = The reflection coefficient R is the ratio of the power of the reflected wave to the Amax Amin Anax power of the incoming wave and is thus proportional to the ratio (BIA). What is the SWR for (a) total reflection and (b) no reflection? (c) For SWR = 1.50, what is R expressed as a percentage? Figure 16-51 Problem 95.arrow_forward
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