4.5- STATIONARY AND PROGRESSIVE WAVES Flashcards
When a guitar string is plucked what is the sound produced dependent on?
way in which string vibrates
What happens if a string on a guitar is plucked gently at its centre?
stationary wave of constant frequency set up on string
When a string on a guitar is plucked at the centre and a stationary wave of constant frequency is set up, what is the frequency of sound produced like?
sound produced has constant frequency
What happens if a guitar string is plucked harshly?
string vibrates in more complicated way + not produced contains other frequencies, as well as frequency produced when plucked gently
When is a stationary wave formed?
when two progressive waves pass through each other
How can a stationary wave be achieved on a string in tension?
by fixing both ends + making middle part vibrate, so progressive waves travel towards each end, reflect at ends, + then pass through each other
What is the simplest stationary wave pattern on a string called?
first harmonic of string
What is the first harmonic of a string sometimes referred to as the strings —?
fundamental mode of vibration
What does the first harmonic of a string consist of?
single loop that has a node at either end
What is a node?
point of no displacement
On the first harmonic of a string, where does the string vibrate with maximum amplitude?
midway between the nodes
What is the point of the first harmonic of a string where there is maximum amplitude referred to as?
antinode
As there are antinodes at the midway of the nodes, how does the string vibrate?
from side to side repeatedly
For the first harmonic pattern to occur, what must the distance between the nodes at either end be like?
must be equal to one half-wavelength of waves on string
Equation for distance between adjacent nodes?
distance between adjacent nodes = 1/2λ
What happens if the frequency of the waves sent along the rope from either end is raised steadily, when the pattern is of a first harmonic?
pattern disappears and new pattern observed with two equal loops along rope
What is the new pattern (second harmonic) observed when the frequency is increased like?
has node at centre + at either end
When is the new pattern observed when frequency is increased formed?
when frequency twice as high, corresponding to half the previous wavelength
What is the distance from one node to the next equal to in the second harmonic?
equal to have a wavelength
If the distance from one to the next is equal to half a wavelength in the second harmonic, what is the length of the rope equal to?
equal to one full wavelength
What do stationary waves that vibrate freely not do?
stationary waves that vibrate freely do not transfer energy to their surroundings
What is the amplitude of vibration at the nodes?
zero
As the amplitude of vibration is zero at the nodes, what does this mean?
no energy at the nodes
Where is the amplitude of vibration a maximum?
at the antinodes
As the amplitude of vibration is a maximum at the antinodes, what does this mean?
maximum energy at antinodes
Why is no energy transferred in a vibrating stationary wave pattern?
because nodes + antinodes are at fixed positions
What happens when two progressive waves are in phase?
reinforce each other to produce large wave
What happens a quarter of cycle when two progressive waves are passing through each other?
two waves have each moved one-quarter of a wavelength in opposite directions- now in antiphase so cancel each other
What happens after a further quarter cycle (now half) when two progressive waves are passing through each other?
two waves back in phase. resultant again a large wave, except reversed
Are the points where there is no displacement fixed in position throughout? (explanation of stationary waves)
yes
What happens between the points of no displacement?
stationary wave oscillates between nodes
How does the amplitude of a vibrating particle in a stationary wave pattern vary with position?
from zero at node to maximum amplitude at antinode
When is the phase difference between two vibrating particles in a stationary wave zero?
if two particles between adjacent nodes or separated by even number of nodes
What is the phase difference between two vibrating particles in a stationary wave 180° (= π radians)?
if two particles separated by odd number of nodes
What is the frequency like in stationary waves?
all particles except those at nodes vibrate at same frequency
What is the frequency like in progressive waves?
all particles vibrate at same frequency
What is the amplitude like in a stationary wave?
amplitude varies from zero at nodes to maximum at nodes
What is the amplitude like in a progressive wave?
amplitude same for all particles
What is the phase difference between two particles in a stationary wave like?
equal to mπ
m- number of nodes between two particles
What is the phase difference between two particles in a progressive wave?
equal to 2πd/λ
d= distance apart
λ= wavelength
What is sound in an air-filled tube or pipe like?
sound resonates at certain frequencies
What happens to resonant frequencies in a pipe closed at one end?
resonant frequencies occur when there is an antinode at open end + node at other end
Where are microwaves from a transmitter directed normally?
at a metal plate
What does the metal plate do when a microwave from a transmitter is directed at it?
reflects microwaves back towards transmitter
When a detector is moved along the line between a microwave transmitter and the metal plate, when is the detector signal found to be zero (or at a minimum?
at equally spaced positions along the line
What do the reflected waves and waves from the transmitter form? (using microwaves)
stationary wave pattern
What is the positions where no signal (or minimum) is detected? (using microwaves)
where nodes occur
How are the nodes spaced? (using microwaves)
at intervals of half a wavelength
