Fundamentals of Physics
10th Edition
ISBN: 9781118230718
Author: David Halliday
Publisher: Wiley, John & Sons, Incorporated
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Chapter 16, Problem 70P
To determine
To find:
The value of
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A 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)
(d)v = 2ghmax
A wave traveling on a string has the following wave function, y(x, t) = Asin(kx + wt + p). At time
t = 0, the point x 0 has a displacement of y(0,0) = 0, and is moving in the negative y -direction.
Which of the following is true about the phase constant and the wave speed direction?
(a) o = "/2, and the wave is moving in the negative x-direction.
(b)y = "2, and the wave is moving in the positive x-direction.
(c) o = n and the wave is moving in the negative x-direction.
(d)g = n and the wave is moving in the positive x-direction.
11)
%3D
%3D
%3D
%3D
Y (90) = Aswyz) =0 or
%3D
Ao las(4)
A standing wave pattern on a string is described by y(x,t) =0.04sin(5πx)cos(40πt), (1) where x and y are in meters and t is inseconds. (a) Determine the locations of all nodes for 0.00 ≦ x ≦0.40m. (b) What is the period of the oscillatory motion of any(nonode) point on the string. (c) What are the speed and theamplitude of the two traveling waves that interfere to produce thiswave? (d) At what times for 0.000 ≦ t ≦ 0.050s will all thepoints on the string have zero transverse velocity?
Chapter 16 Solutions
Fundamentals of Physics
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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- (d)v = 2/ghmax A wave traveling on a string has the following wave function, y(x, t) = Asin(kx + wt + p). At time 3D0, the point x = 0 has a displacement of y(0,0) = 0, and is moving in the negative y-direction. Which of the following is true about the phase constant and the wave speed direction? (a) o = "/2, and the wave is moving in the negative x-direction. (b) = "/2, and the wave is moving in the positive x -direction. 11) %3D (c) o = n and the wave is moving in the negative x -direction. (d)o = n and the wave is moving in the positive x -direction. 12) Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is Lanswer below ) that ofwave B. (a) half (b)twice (c) one-fourth (d) four timesarrow_forwardA transverse wave on a string has amplitude 0.300 cm wavelength 12.0 cm, and speed 6.00 cm/s. It is represented by equation y(x,t)=Acos[2π/λ(x−vt)] At time t = 0, compute y at 1.5-cm intervals of x (that is, at x = 0, x = 1.5cm, x = 3.0cm, and so on) from x = 0 to x= 12.0cm. Graph the results. This is the shape of the string at time t = 0. How to do the graph?arrow_forwardA guitar string obeys the linear wave equation with wave-speed u, and is fixed at x = 0 and x = L. It is pulled out into a parabolic shape, and then released at time t = 0, so that immediately afterwards the transverse displacement at a position a along the string is given by y(x,0) = Ax (L- x). (a) Sketch a graph of y(x, 0). (b) The initial displacement y(x, 0) is now represented as a sum of harmonics, (TTT). y(x,0) = anyn(x), Yn (x) = sin n=1 For the above form of y(x, 0), find an expression for the Fourier coefficients an (c) Hence, and assuming that the string is released from rest, write down an expres- sion for y(x, t), the transverse displacement profile of the string at an arbitrary later time.arrow_forward
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