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Key Points:
*Waves carry energy
As a wave travels along a string, air or any medium
form, energy is created and travels through the medium.
We can consider this as a wave is a motion of energy
through a medium
*The wave travels through the medium
A wave does not carry its medium with it, instead,
the medium willmove out of its equilibrium position.
For example, during an earthquake, damage to
surroundings is caused due to the ground moving out of
equilibrium.
Consider:
 What is a pulse?
A pulse can be defined as an equilibrium
disturbance in a wave for a short duration. For example,
a single knock on a door creates a sound pulse that lasts
a short amount of time.
If a string is held under constant tension, we can
analyze the motion of the string with respect to a point.
Calculatingvariables in a Pulse In 1D
*The equilibrium of a pulse is denoted by
D(x, t)
D = displacement from equilibrium (m)
x = position (m)
t= time (s)
*We can use this equation to describe a waveform. At a
certaintime during a pulse, different waveforms are
present.
*Consider the function D(x, t) =
6
𝑥2+4
*If a pulse has a position of x = 2.0m at 0.0s, what is the
equation?
Answer:
x=2.0m, t=0.0s:
D(2.0m, 0.0s) =
6
(2.0𝑚)2+4
DISPLACEMENT FUNCTION
*How about at 1.5s if it is moving at 3.0m/s to the left?
At any speed, we can substitute x for (x-vt).
Why?
If at t=0, the wave of a pulse is moving at an increasing x
with speed v, then we can make this substitution. This is
called the displacement function
Answer:
D(x, 1.5s) =
6
( 𝑥−𝑣𝑡)2+4
Plug in t=1.5s and v = -3.0m/s
D(x, 1.5s) =
6
( 𝑥+3.0(1.5))2+4
*Remember, since x-vt represents a positive velocity,
x+vt will represent a negative velocity.
peak
Example of a waveform
function when t=1.0s
Try:
A travelling pulse is given by:
D(x, t) =
2.0
( 𝑥−3.0𝑡)4+5.0
a) What is the velocity of the pulse?
b) What is the displacement of a point on the medium
at x = 1.5m at t=2.0s
Answer:
a) remember, x-vt
velocity = 3.0m/s to the right
b)Plug in values:
D(1.5, 2.0) =
20.0
(1.5−3.0(2.0))4+5.0
D = 4.8e-2m
Learning ob 1

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Learning ob 1

  • 1. Key Points: *Waves carry energy As a wave travels along a string, air or any medium form, energy is created and travels through the medium. We can consider this as a wave is a motion of energy through a medium *The wave travels through the medium A wave does not carry its medium with it, instead, the medium willmove out of its equilibrium position. For example, during an earthquake, damage to surroundings is caused due to the ground moving out of equilibrium.
  • 2. Consider:  What is a pulse? A pulse can be defined as an equilibrium disturbance in a wave for a short duration. For example, a single knock on a door creates a sound pulse that lasts a short amount of time. If a string is held under constant tension, we can analyze the motion of the string with respect to a point.
  • 3. Calculatingvariables in a Pulse In 1D *The equilibrium of a pulse is denoted by D(x, t) D = displacement from equilibrium (m) x = position (m) t= time (s) *We can use this equation to describe a waveform. At a certaintime during a pulse, different waveforms are present. *Consider the function D(x, t) = 6 𝑥2+4 *If a pulse has a position of x = 2.0m at 0.0s, what is the equation? Answer: x=2.0m, t=0.0s: D(2.0m, 0.0s) = 6 (2.0𝑚)2+4
  • 4. DISPLACEMENT FUNCTION *How about at 1.5s if it is moving at 3.0m/s to the left? At any speed, we can substitute x for (x-vt). Why? If at t=0, the wave of a pulse is moving at an increasing x with speed v, then we can make this substitution. This is called the displacement function Answer: D(x, 1.5s) = 6 ( 𝑥−𝑣𝑡)2+4 Plug in t=1.5s and v = -3.0m/s D(x, 1.5s) = 6 ( 𝑥+3.0(1.5))2+4 *Remember, since x-vt represents a positive velocity, x+vt will represent a negative velocity. peak Example of a waveform function when t=1.0s
  • 5. Try: A travelling pulse is given by: D(x, t) = 2.0 ( 𝑥−3.0𝑡)4+5.0 a) What is the velocity of the pulse? b) What is the displacement of a point on the medium at x = 1.5m at t=2.0s Answer: a) remember, x-vt velocity = 3.0m/s to the right b)Plug in values: D(1.5, 2.0) = 20.0 (1.5−3.0(2.0))4+5.0 D = 4.8e-2m