Learning Goal:To gain an understanding of constructive and destructive interference.Consider two sinusoidal waves (1 and 2) of identical wavelength A, period T, andmaximum amplitude A. A snapshot of one of these waves taken at a certain time isdisplayed in the figure below. (Figure 1) Let y₁ (z, t) and y2 (x, t) represent thedisplacement of each wave at position at time t. If these waves were to be in the samelocation (2) at the same time, they would interfere with one another. This would result in asingle wave with a displacement y (z, t) given byy(z, t) = y₁ (z, t) + y₂(z, t).This equation states that at time t the displacement y (x, t) of the resulting wave atposition z is the algebraic sum of the displacements of the waves 1 and 2 at position z attime t. When the maximum displacement of the resulting wave is less than the amplitudeof the original waves, that is, when y/max < A, the waves are said to interfere destructivelybecause the result is smaller than either of the individual waves. Similarly, whenymax > A, the waves are said to interfere constructively because the resulting wave islarger than either of the individual waves. Notice that 0≤ ymax ≤ 2A.FigureBA.DCSaufco23 of 3 Part CNow look at the waves emitted from two identical sources (e.g., two identical rocks that fall into a lake at the same time). The sources emit identical waves at the exact same time. (Figure 3)Identify whether the waves interfere constructively or destructively at each point A to D.For points A to D enter either c for constructive ord for destructive interference. For example if constructive interference occurs at points A, C and D, and destructive interference occurs at B, entercdcc.▸ View Available Hint(s)Submit

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Identify whether the waves interfere constructively or destructively at each point A to D.

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 27CQ: Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is...

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Wave Motion

A wave motion is defined as the propagation of disturbances or transfer of energy and momentum from the state of rest or equilibrium to another point in a medium without any actual transfer of matter between them. In a simple explanation, it is the propagation of energy through a medium that is produced due to the repeated vibrations of the particles. Common things we see day to day like waves on water oscillation of a pendulum or bell, light wave, and all the subatomic particles exhibiting wavelike properties. The propagation of waves depends on the medium and their properties. The wave function is the disturbance that produces waves as a function of time. This disturbance oscillates periodically with a fixed frequency and wavelength. There are linear wave motion and non-linear wave motion based on their propagation, motion, and time period where linear wave motion is like sinusoidal waves and non-linear wave motion like a wave motion that gets interrupted in the middle of their propagation.

Question

Learning Goal:
To gain an understanding of constructive and destructive interference.
Consider two sinusoidal waves (1 and 2) of identical wavelength A, period T, and
maximum amplitude A. A snapshot of one of these waves taken at a certain time is
displayed in the figure below. (Figure 1) Let y₁ (z, t) and y2 (x, t) represent the
displacement of each wave at position at time t. If these waves were to be in the same
location (2) at the same time, they would interfere with one another. This would result in a
single wave with a displacement y (z, t) given by
y(z, t) = y₁ (z, t) + y₂(z, t).
This equation states that at time t the displacement y (x, t) of the resulting wave at
position z is the algebraic sum of the displacements of the waves 1 and 2 at position z at
time t. When the maximum displacement of the resulting wave is less than the amplitude
of the original waves, that is, when y/max < A, the waves are said to interfere destructively
because the result is smaller than either of the individual waves. Similarly, when
ymax > A, the waves are said to interfere constructively because the resulting wave is
larger than either of the individual waves. Notice that 0≤ ymax ≤ 2A.
Figure
B
A.
D
C
Saufco2
3 of 3

Part C
Now look at the waves emitted from two identical sources (e.g., two identical rocks that fall into a lake at the same time). The sources emit identical waves at the exact same time. (Figure 3)
Identify whether the waves interfere constructively or destructively at each point A to D.
For points A to D enter either c for constructive ord for destructive interference. For example if constructive interference occurs at points A, C and D, and destructive interference occurs at B, enter
cdcc.
▸ View Available Hint(s)
Submit

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