Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated
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Chapter 16, Problem 11Q
To determine
To find:
To rank the waves according to the amplitude of the net wave.
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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.
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)
*27 O A sinusoidal wave is sent along a string with a linear
density of 2.0 g/m. As it travels, the kinetic energies of
the mass elements along the string vary. Figure 16-37a gives the
rate dKldt at which kinetic energy passes through the string ele-
ments at a particular instant, plotted as a function of distance x
along the string. Figure 16-37b is similar except that it gives the
rate at which kinetic energy passes through a particular mass ele-
ment (at a particular location), plotted as a function of time t. For
both figures, the scale on the vertical (rate) axis is set by R, = 10 W.
What is the amplitude of the wave?
R,
0.1
0.2
x (m)
t (ms)
(a)
(b)
Chapter 16 Solutions
Fundamentals of Physics Extended
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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- A string with a mass of 0.30 kg has a length of 4.00 m. If the tension in the string is 50.00 N, and a sinusoidal wave with an amplitude of 2.00 cm is induced on the string, what must the frequency be for an average power of 100.00 W?arrow_forwardTwo sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is =0.075 kg/m and the tension in the string is FT=5.00 N. The time interval between instances of total destructive interference is t=0.13 s. What is the wavelength of the waves?arrow_forwardConsider two sinusoidal waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x+3s1t) and y2(x,t)=0.6msin(8m1x6s1t) . What is the height of the resultant wave formed by the interference of the two waves at the position x=0.5 m at time t=0.2 s?arrow_forward
- A guitar string is 90.0 cm long and has a mass of 3.16 g. From the bridge to the support post there is 60.0 cm and the rope is under a tension of 520 N. Determine: a) The linear density of the string and the speed of the waveb) The wavelength of the first harmonicc) The frequency of the first harmonicarrow_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_forward2 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)arrow_forward
- 6 GO A sInusoidal wave travels 0.2 along a string under tension. Figure 16-31 gives the slopes x (m) along the string at time t= 0. The scale of the x axis is set by x, = 0.80 m. What is the amplitude of -0.2 Figure 16-31 Problem 6. the wave?arrow_forwardVerify by direct substitution that the wave function for a standing wave given by: y= (2A cos kx) cos wt is a solution of the general linear wave equation: 1 a?y ax?arrow_forward106 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_forward
- The profile of a transverse harmonic wave, traveling at 1.2 m/s on a string, is given by y = (0.02m)sin(157m-1)x %3D Determine its amplitude, wavelength, frequency and period.arrow_forwardThe tension in a wire clamped at both ends is increased to 5.1 times its original magnitude without appreciably changing the wire's length between the clamps. What is the ratio of the new to the old wave speed for transverse waves traveling along this wire?arrow_forwardFigure 12–32 shows various positions of a child on a swing moving toward a person on the ground who is blowing a whistle. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning. Whiśtle Whistle, A В FIGURE 12-32 Question 17.arrow_forward
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