Harmonic Waves
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Harmonic Waves: Understanding Sinusoidal Behavior, Wave Speed, and Wave Power, Slides of Physics
An in-depth exploration of harmonic waves, focusing on their sinusoidal behavior, wave speed, and wave power. Topics covered include the relationship between frequency, wavelength, and wave speed, as well as the calculation of wave power using the energy equation. Real-world examples are used to illustrate the concepts.
Typology: Slides
2012/2013
1 / 8
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Harmonic Waves
Sinusoidal Behavior
An harmonically oscillatingpoint is described by a sinewave.•
y^
=^
A
cos
t
An object can take asinusoidal shape in space.•
y^
=^
A
cos
kx
1 period 1 wavelength
y y
t x Docsity.com
Wave Speed
The speed is related tothe wavenumber•
v^
=^
/
T
-^
v^
= (
k
2
-^
v =
/ k
The wavenumber isrelated to the speed•
k^
= 2
=
/ v
Seasick
While boating on the oceanyou see wave crests 14 mapart and 3.6 m deep. Ittakes 1.5 s for a float to risefrom trough to crest.
What is the wave speed?
The time from trough to crestis half a period:
T
= 3.0 s.
The wavelength is
= 14 m.
The speed can be founddirectly:
v
/ T
= 4.7 m/s.
Intensity
Intensity of a wave is the rateenergy is carried across asurface area.
This is true for linear andother waves.
For a spherical wave, theintensity
I^
P/A
P
r
2
Find the power from thespeed and frequency.
Now use the equation forpower•
P
= 11 W
Rope Snake
A garden hose has 0.44 kg/m.A child pulls it with a tension of12 N, then shakes it side toside to make waves with 25 cmamplitude at 2.0 cycles persecond.
What is the power supplied bythe child?
(^1) - s (^6). 12
2
m/s (^2). 5
/^
F^ f
v^
T
next
v
A
P
2 2
1 ^2