Standing Waves And Beats
Standing Waves & Overtones
Beats
1. Boundaries & Geometry
Left End Boundary:
Closed (Fixed Node)
Open (Free Antinode)
Right End Boundary:
Closed (Fixed Node)
Open (Free Antinode)
Length
L
(m):
Fundamental Wavelength λ
1
(m):
2. Medium Properties
Tension
T
(N):
Linear Density μ (kg/m):
Calculated Velocity
v
= √
(
T
/μ)
(m/s):
3. Frequency & View Controls
Fundamental Frequency
f
1
(Hz):
View Zoom Scale:
1.00x
Reset View & Pos
Top View: 1
st
Harmonic (Fundamental Mode / 0
th
Overtone)
Incident (Left→Right)
Reflected (Right→Left)
Node (N)
Antinode (AN)
Drag to pan view | Click to select nearest Node / Antinode
Velocity Equation
v
= √
(
T
/ μ)
= 440.00 m/s
1
st
Harmonic Formula (
Closed - Open
)
L
=
λ
1
4
⇒ λ
1
= 4
L
Selected Mode (
3
rd
Harmonic / 1
st
Overtone
)
λ
n
= 0.333 m |
f
n
= 1320.0 Hz
Overtone Mode Selector
3
rd
Harmonic (1
st
Overtone)
Shows Mode Index
n
and corresponding
n
-1 Overtone designation.
Bottom View: 3
rd
Harmonic (1
st
Overtone)
Incident (Left→Right)
Reflected (Right→Left)
Node (N)
Antinode (AN)
Drag to pan view | Click to select nearest Node / Antinode
1. Wave Frequencies
Frequency
f
1
(Hz):
Frequency
f
2
(Hz):
2. Amplitude & Zoom
Amplitude
A
1
(%):
Amplitude
A
2
(%):
View Zoom Scale:
1.00x
3. Playback Controls
Pause
Fast Forward
Rewind
Reset View & Pos
Simulation Speed:
Beat Frequency
f
beat
= |
f
1
-
f
2
| = 4.0 Hz
Envelope Frequency
f
env
=
|
f
1
-
f
2
|
2
= 2.0 Hz
Individual Component Waves
y
1
(
t
) and
y
2
(
t
)
Wave 1 (
f
1
)
Wave 2 (
f
2
)
Drag to pan view | Click to inspect point value
Superposition Wave Beat Result:
y
(
t
) =
y
1
(
t
) +
y
2
(
t
)
Sum Signal
y
(
t
)
Beat Envelope
Drag to pan view | Click to inspect point value