1) Standing waves on strings occur when the string vibrates in place without propagating, forming regions of nodes with little motion and antinodes with maximum motion. 2) Standing waves require the driving frequency to match the natural frequency of the string, known as resonance. 3) Harmonics occur at integer multiples of the fundamental frequency, with wavelengths that are simple fractions of the fundamental wavelength. The fundamental harmonic starts the propagation.

1. Standing Waves On
Strings
MEERWISE JOYA
PHYSICS 101
LEARNING OBJECT

2. “
”
Sometimes when you vibrate a string it's possible to get it to vibrate in a way such that you're generating
a wave, but the wave doesn't propagate. It just sits there and vibrates up and down in place. Such a
wave is called a standing wave
Notice wave does not travel but just move up and down

3. In previous chapters we have seen travelling waves have regions known as
crests (high points) and troughs (low points). Standing waves don't go
anywhere, but they do have regions where the position of the wave is very
small, almost zero. These regions are called nodes. There are also regions
where the position is very intense, greater than anywhere else in the wave,
called antinodes.

4. https://www.yout
ube.com/watch?
v=DaWsgmsTFAs
STANDING WAVES DON'T FORM JUST
UNDER AND CIRCUMSTANCE. THEY
REQUIRE THAT ENERGY PUT INTO SYSTEM
TO BE AT AN APPROPRIATE FREQUENCY.
THAT IS; WHEN THE DRIVING FREQUENCY
IN SYSTEM EQUALS THE NATURAL
FREQUENCY OF THE STRING. THIS
CONDITION IS KNOWN AS RESONANCE.
I recommend you watch video of
Tacoma Narrow Bridge collapsing
demonstrating resonance frequency
and its consequences

5. WHEN THE FREQUENCY OF THE STRING IS EXACT THIS IS WHEN THE STRING BEGINS TO PROPAGATE UP AND DOWN THIS IS
KNOWN AS A HARMONIC
BUT IN ANY SYSTEM WHERE A STANDING WAVE CAN FORM THERE ARE SEVERAL HARMONICS WHICH CAN OCCUR
FIRST HARMONIC IS KNOWN AS THE FUNDAMENTAL HARMONIC (FUNDAMENTAL IN STARTING THE PROPAGATION, HENCE
THE NAME FUNDAMENTAL HARMONIC) AND SUBSEQUENTLY THE REST KNOWN AS SECOND, THIRD, FOURTH HARMONIC
THE WAVELENGTHS OF THE HARMONICS ARE SIMPLE FRACTIONS OF THE FUNDAMENTAL WAVELENGTH. IF THE
FUNDAMENTAL WAVELENGTH WERE 2 M THE WAVELENGTH OF THE SECOND HARMONIC WOULD BE 1 M, THE THIRD
HARMONIC WOULD BE 2⁄3 M, THE FOURTH 1⁄2 M, AND SO ON
FREQUENCY IS INVERSELY PROPORTIONAL TO WAVELENGTH. THE FREQUENCIES OF THE HARMONICS ARE MULTIPLES OF
THE FUNDAMENTAL FREQUENCY. IF THE FUNDAMENTAL FREQUENCY WERE 2 HZ THE FREQUENCY OF THE SECOND
HARMONIC WOULD BE 4 HZ, THE THIRD HARMONIC WOULD BE 6 HZ, THE FOURTH 8 HZ, AND SO ON.
Formula for
frequency and
wavelength
L=Length
T=Tension
M=Linear mass
density

6. A guitar string is 1m long and has a linear mass density of 2kg/m. The tension in the string is 90N.
What is the fundamental frequency?
 Wavelength is 2L, so 2x1m=2m
 Linear mass density is 2kg/m
 Tension in the string is 90N
 Fundamental frequency is unknown
We can go ahead and use
this equation
F1=(1/2m)(sqrt(90N/2kg/m))
=3.35 Hz