phys 101 lo6 - shushan deng
Post on 08-Aug-2015
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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
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
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
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
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
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?
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