chapter 4.5 -4.7 stationary and progressive waves

how is a stationary wave formed

when 2 waves pass through each other

the first harmonic / the fundamental mode of vibration

the simplest stationary wave pattern - consists of a single loop that has a node at either end, and the wave vibrates with maximum amplitude midway between the nodes

antinode

the point of maximum amplitude on a stationary wave midway between 2 nodes

equation for distance between adjacent nodes

1/2 λ

why do stationary waves the vibrate freely not transfer energy to their surroundings

because the nodes and antinodes are at fixed positions - the amplitude of vibration remains same at nodes and antinodes, so energy at each remains the same

the amplitude of a vibrating particle in a stationary wave pattern

varies with position from zero at a node to maximum amplitude at an antinode

the phase difference between 2 vibrating particles in a stationary wave pattern if the particles are between adjacent nodes or separated by an even number of nodes

zero

the phase difference between 2 vibrating particles in a stationary wave pattern if the particles are either side of a node or separated by an odd number of nodes

180 degrees = π radians

frequency of particles in stationary waves

all particles except those at the nodes vibrate at the same frequency

frequency of particles in progressive waves

all particles vibrate at the same frequency

amplitude in stationary waves

amplitude varies from zero at the nodes to a maximum at the antinodes

amplitude in progressive waves

amplitude is same for all particles

phase difference between 2 particles in stationary waves

equal to mπ, where m = number of nodes between the 2 particles

phase difference between 2 particles in progressive waves

equal to 2πd/λ, where d = distance apart, and λ = wavelength

at what frequency is the first harmonic pattern of vibration seen

at the lowest possible frequency that gives a pattern

equation for the wavelength of the waves that form the first harmonic pattern of vibration

λ = 2L

equation for the first harmonic frequency

f = c/λ = c/2L

the general formula for the frequency at which wave patterns occur

f, 2f, 3f, 4f...., where f = the first harmonic frequency of the fundamental vibrations

key condition for a stationary wave to form

the time taken for a wave to travel along a string and back should be equal to the time taken for a whole number of cycles of the vibrator

equation for the time taken for a wave to travel along a string and back

t = 2L/c

equation for a vibrator to pass through a whole number of cycles

m / f

equation for the length of the vibrating section of a string

L = mλ / 2

what does the pitch of a note correspond to

frequency - so the pitch of a note from a stretched string can be altered by changing the tension of the string or by altering its length

how can pitch be increased by changing the tension or the length of a string

by raising the tension, or by shortening the length

how can pitch be decreased by changing the tension or the length of a string

by lowering the tension, or by increasing the length

equation showing that the first harmonic frequency depends on the tension in the wire and its mass per unit length

f = (1/2L) x (sq. root T/mass per unit length)

what is the position of the spot of light on the screen of an oscilloscope affected by

the pd across either pair of deflecting plates - the displacement of the spot is proportional to the applied pd --> no pd = no movement of spot; applied pd = spot deflects horizontally

how are the X-plates on an oscilloscope used to display a waveform

the X-plates are connected to the oscilloscope's time base circuit, which makes the spot move at constant speed left to right across the screen, and then back again much faster - calibrated in ms or microseconds per cm

how are the Y plates on an oscilloscope used to display a waveform

the Y-plates are connected to the pd via the Y-input so the spot moves up and down as it moves left to right across the screen, tracing out the waveform on the screen - calibrated in volts per cm

why can the x-scale on an oscilloscope be calibrated

because the spot moves at constant speed across the screen

why can the Y-input on an oscilloscope be calibrated in volts per cm

because the vertical displacement of the spot is proportional to the pd applied to the Y-plates