L4
Transverse Waves
revisitedReflection, Interference,
Standing Waves on String
Transverse wave propagation
Wave reflection at a fixed end:
the restoring force in the
boundary material causes an
upward pulse to become a
downward pulse upon
reflection
Wave reflection at an open end:
the upward pulse maintains its
orientation upon reflection
PhET Simulation
Wave on a String
Wave Interference/
Wave Superposition
Ct 4.5.2.sup
The pulse on the left is moving right, the pulse
on the right is moving left. What do you see at
the "central moment" they pass through one
another?
Ct 4.5.2.sup
A
B
D
C
E
SIM
www.physics.nyu.edu/~ts2/Animation/waves.html
Suppose the pulse reflected from a
boundary and moving to the left
seen earlier meets another pulse
moving to the right…
Identical
waves
moving
in
opposite
directions
Motion
of
point
along
the
spring
Understanding Reflection using
Superposition
The physics of waves is local – each spot in the
medium (i.e. the rope) is only influenced by
the spots next to it
This means that a fixed rope obeys the same
physics as an infinite rope, with one exception:
the point at the end, a.k.a. the boundary
If we take a pulse on an infinite rope, and add
an inverted mirror image of the pulse
travelling in the other direction, it is
guaranteed to interfere destructively so that
the center point does not move.
If the center
does not move,
the left side
looks exactly as
if it had
reflected off a
fixed boundary
This way of
thinking about
reflection is the
method of
images
Boundary for free end
Slope = difference in tension = one part of rope
pulling on the other
At end, there’s nothing to pull on, so rope
must be flat
To make this
using images, we
think of a mirrorimage pulse
that’s not
inverted
Wave reflection simulation:
http://www.walterfendt.de/ph14e/stwaverefl.htm
Reflection off of two boundaries
• It’s like looking at yourself in two mirrors –
you must use infinite images!
• If you try to fit in a wave with the wrong
wavelength, all the infinite images have
destructive interference and give zero – only
waves with nodes at the walls work!
Standing wave Applet
http://webphysics.davidson.edu/A
pplets/superposition/default.html
(Example 2)
Standing wave representation
Standing Waves
in a Stretched String
Conditions for standing waves
Recall that
f=v/λ
Hence
fn =n f1
where f1 = v/(2L)
f1 is called the fundamental frequency (the
lowest possible frequency)
All harmonics (n= 1,2,3,…) are possible
excitations for a string held at both ends!
f2 is called the 2nd harmonic, and
is also sometimes referred to as
st
the 1 overtone (especially in
reference to sound).
f3 is the 3d harmonic or the 2nd
overtone, etc.
Recall that v=f λ.
Suppose we keep v and the length of
the string constant.
Can we establish a standing wave if we
increase the vibrating frequency from
f1 to 1.2 f1?
A) yes
B) no
C) sometimes
D) Not enough information given
Standing Waves on a String
(rope)
Demo