The nodes of a standing wave are points where the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move). Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(x, t) = A cos(kx) sin(wt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, w is the angular frequency of the wave, and t is time.
The nodes of a standing wave are points where the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move). Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(x, t) = A cos(kx) sin(wt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, w is the angular frequency of the wave, and t is time.
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter16: Waves
Section: Chapter Questions
Problem 91P: Consider two sinusoidal sine waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x+3s1t+3)...
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![• What is the displacement of the string as a function of x at time T/4, where T is the period of oscillation of the
string?
• At which three points X₁, X2, and x3 closest to x = 0 but with x > 0 will the displacement of the string y (x, t) be
zero for all times? These are the first three nodal points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03aa51a1-720a-4e9c-8893-1076874d72cf%2Fa184670d-30c1-4aaa-bd77-3e4311acad44%2F9h6o5yl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:• What is the displacement of the string as a function of x at time T/4, where T is the period of oscillation of the
string?
• At which three points X₁, X2, and x3 closest to x = 0 but with x > 0 will the displacement of the string y (x, t) be
zero for all times? These are the first three nodal points.
![The nodes of a standing wave are points where the displacement of the wave is zero at all
times. Nodes are important for matching boundary conditions, for example that the point at
which a string is tied to a support has zero displacement at all times (i.e., the point of
attachment does not move).
Consider a standing wave, where y represents the transverse displacement of a string that
extends along the x direction. Here is a common mathematical form for such a wave:
y(x, t) = A cos(kx) sin(wt),
where A is the maximum transverse displacement of the string (the amplitude of the
wave), which is assumed to be nonzero, k is the wavenumber, w is the angular frequency
of the wave, and t is time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03aa51a1-720a-4e9c-8893-1076874d72cf%2Fa184670d-30c1-4aaa-bd77-3e4311acad44%2Fgwuhq7j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The nodes of a standing wave are points where the displacement of the wave is zero at all
times. Nodes are important for matching boundary conditions, for example that the point at
which a string is tied to a support has zero displacement at all times (i.e., the point of
attachment does not move).
Consider a standing wave, where y represents the transverse displacement of a string that
extends along the x direction. Here is a common mathematical form for such a wave:
y(x, t) = A cos(kx) sin(wt),
where A is the maximum transverse displacement of the string (the amplitude of the
wave), which is assumed to be nonzero, k is the wavenumber, w is the angular frequency
of the wave, and t is time.
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