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what is a stationary wave?
not a single wave
formed when two progressive waves with the same frequency travelling in opposite directions are superposed
as they have the same frequency, at certain points they are in phase or in antiphase
at antiphase, their displacements cancel out, forming a node, a point where the displacement is always 0
at points when the waves are in phase, an antinode is formed, with the greatest amplitude and intensity
do stationary waves transfer energy?
no
what does the separation between two nodes represent?
half the wavelength of the original progressive wave
what is the frequency of a stationary wave?
the same as the progressive waves that formed it
what is the phase difference along a stationary wave?
all the particles between two nodes in a stationary wave are oscillating in phase with each other
they all reach their maximum positive displacement at the same time
however, their amplitude differs, with the maximum amplitude at the antinode
on opposite sides of a node, the particles are in antiphase with a phase difference of pi radians
particles on one side reach their maximum positive displacement when particles on the other side reach their maximum negative displacement
what are the similarities and differences between stationary and progressive waves?
progressive waves transfer energy but stationary waves don’t
in progressive waves, wavelength is the distance between two adjacent points in phase, but in stationary waves, wavelength is double the distance between two nodes
in progressive waves, phase difference is measured as a proportion of the cycle of the wave, but in stationary waves, all points between two nodes are in phase, and in opposite sides of a node they are in antiphase
in progressive waves, all parts of the wave have the same amplitude, but in stationary waves, the maximum amplitude occurs at the antinode then drops to 0 at the node
what does the resultant wave look like when time= an odd number of quarter periods?
a flat line so displacement is 0
what does the resultant wave look like when time= a whole number of half periods?
you know like a normal looking wave
what is the fundamental frequency?
the minimum frequency of a stationary wave for a string
it depends on mass, tension and length
how do stationary waves form on strings?
if a string is stretched between two fixed points, the points act as nodes
when the string is plucked a progressive wave travels along the string and reflects off its ends
this creates two progressive waves travelling in opposite directions which then form a stationary wave
when the string is plucked, it vibrates in its fundamental mode of vibration where the wavelength is double the length of the string
what are harmonics?
stationary waves formed when the frequency is higher than the fundamental mode of frequency
at each harmonic, the frequency is an integer multiple of the fundamental frequency
when tension is constant, speed is constant
therefore due to v= f lamda as the frequency increases the wavelength decreases in proportion
on a string, when the frequency = 3*f0, what is the wavelength?
2/3 L
on a string, when the frequency = 5*f0, what is the wavelength?
2/5 L
what determines the stationary wave formed in an air column?
the fundamental frequency of the tube, whether the ends are open or closed, and the length of the tube
what happens when one end of the tube is closed and one end is open?
there will be a node at a closed end, because the air at the closed end cannot move, and an antinode at the open end because the oscillations of the air are at their greatest displacement
how many wavelengths are in the fundamental mode of vibration in a closed-open tube?
1/4
?in the 4th harmonic of a open-closed tube, how many wavelengths are there?
7/4
what is the frequency of harmonics of a open-closed tube?
an odd multiple of the fundamental frequency
what happens when both ends of the tube are open?
both ends have antinodes
how many wavelengths are in the fundamental frequency of a open-open tube?
1/2
in the 4th harmonic of an open-open tube, how many wavelengths are there
2
what are the frequencies of harmonics in an open-open tube?
all integer multiples of the fundamental frequency
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