Standing waves occur when vibrations move back and forth along a taut string or medium. Nodes remain fixed in place with zero amplitude, while anti-nodes oscillate with maximum amplitude. Harmonics refer to the frequencies of standing waves, with the fundamental frequency being the lowest. The third harmonic frequency is three times the fundamental frequency. Nodes experience destructive interference which causes their zero displacement. If the distance between the first and fourth nodes of a standing wave on a guitar string is 40 cm, then the original wave's wavelength is 26.7 cm.
2. WHAT IS A STANDING WAVE?
A standing wave is a vibration in
which certain points of the wave
remain fixed, while other points
oscillate to maximum amplitude.
The nodes of a standing wave
remain at amplitude=0, while the
points between the nodes (the
anti-nodes) move with maximum
amplitude
3. WHAT CAN CAUSE A STANDING
WAVE PATTERN?
Standing wave patterns can occur
when vibrations move along a
taut string.
Waves are reflected back and
forth between the fixed ends of
the string, when the string is
plucked or disturbed
An example of this can be found
in plucking guitar strings
4. STANDING WAVES ON STRINGS
Harmonics refer to the associated patterns
and frequencies of the standing waves
The fundamental frequency, also known as
first harmonic, is the lowest frequency of
the standing wave pattern
The equation for frequency, f, can be given
as such: f = √(T/µ) where T=Tension and
µ=linear mass density
Fundamental, first harmonic
Second harmonic
n=1
n=2
5. QUESTION 1
The answer is c) 450 Hz.
This is because the frequency of a
harmonic is “n” times the
frequency of the fundamental,
where “n” is an integer. A
frequency of the third harmonic
would be 3 times the value of the
fundamental.
f3 = 3*f1 = 3*150 Hz = 450 Hz.
The fundamental frequency of a
stretched string is 150 Hz.The
frequency of the third harmonic
is ________.
a) 250 Hz
b) 350 Hz
c) 450 Hz
d) 550 Hz
6. QUESTION 2
The answer is b) Destructive
interference
Since nodes always remain at
amplitude=0, their displacement
also remains at zero.This zero
displacement is possible because
of destructive interference.
A node is a point along the wave
in which there is ________.
a) Maximum amplitude
b) Destructive interference
c) Constructive interference
7. QUESTION 3
We know that the distance
between consecutive nodes is half
a wavelength. From the first and
fourth nodes, the distance is one
and a half (1.5) wavelengths.
(40.0 cm / 1.5 ) = 26.7 cm
The wavelength of the original
wave is 26.7 cm.
A person playing guitar creates a
standing wave by plucking a string.
If the distance between the first
and fourth nodes is 40.0 cm, then
what is the wavelength of the
original wave?
