stationary waves

Question 1

how are stationary waves produced?

Answer 1

standing (stationary waves) are produced by the superposition of two progressive waves of the same frequency, wavelength and amplitude travelling in opposite directions

Question 2

how is the formation of a stationary wave achieved?

Answer 2

by a travelling progressive wave being reflected

Question 3

state the difference between stationary waves and progressive waves in terms of energy

Answer 3

stationary waves store energy whereas progressive waves transfer energy.

Question 4

explain, in terms of interference, what happens to stationary waves upon formation using a graph of displacement against position

Answer 4

• at the start of cycle, waves interfere destructively (zero displacement)
• 1/4 cycle later, waves overlap and interfere constructively (the stationary waves amplitude is 2x therefore - peak then trough)
• 1/2 cycle, waves interfere destructively (zero displacement)
  3/4 cycle, waves overlap and interfere constructively (amplitude 2x, trough peak)

Question 5

briefly describe how you would demonstrate the formation of stationary waves

Answer 5

setting up a driving oscillator at one end of a stretched string with the other end fixed
the wave generated by the oscillator is reflected back and forth and

Question 6

compare progressive and stationary waves in terms of amplitude

Answer 6

progressive waves - all points have the same amplitude in turns therefore
stationary waves - each point has a different amplitude depending on the amount of superposition

Question 7

compare progressive and stationary waves in terms of wavelength

Answer 7

progressive - points exactly a wavelength apart are in phase, the phase of points of about one wavelength vary from 0-360 degrees
stationary - points between nodes are in phase. points on either side of a node are out of phase

Question 8

compare progressive and stationary waves in terms of nodes/antinodes

Answer 8

progressive waves do not have nodes/antinodes whereas stationary waves do

Question 9

compare progressive and stationary waves in terms of wavespeed

Answer 9

progressive waves - the wavespeed is the speed at which the wave moves through a medium
stationary waves -

Question 9

compare progressive and stationary waves in terms of wavespeed

Answer 9

progressive waves - the wavespeed is the speed at which the wave moves through a medium
stationary waves - each point of a wave oscillates at a different speed. the overall wave does not moves

Question 10

what is a stationary wave made up of

Answer 10

it is a transverse wave (each particle vibrates at right angles to the string) and has nodes and antinodes

Question 11

what are nodes?

Answer 11

nodes are points on the wave where the amplitude of the vibration is zero

Question 12

what are antinodes?

Answer 12

antinodes are points on the wave where the vibrations are at their maximum amplitude

Question 13

why do nodes and antinodes do not moves on the string?

Answer 13

Nodes are fixed and antinodes only move in the vertical direction

Question 14

what is the phase difference of a stationary wave?

Answer 14

The phase difference between two points on a stationary wave are either in phase or out of phase Points between nodes are in phase with each other
Points that have an odd number of nodes between them are out of phase
Points that have an even number of nodes between them are in phase

Question 15

what type of interference occurs at a node?

Answer 15

the waves are in antiphase therefore total destructive interference because the displacements of the two waves canacel eachother out always

Question 16

what type of interference occurs at an antinode?

Answer 16

the waves are in phase so constructive interference because the displacements of the two waves combine to make a bigger displacement

Question 17

how can you calculate the wavelength of a stationary wave?

Answer 17

number of loops / 2

Question 18

explain how you would demonstrate stationary waves through microwaves

Answer 18

a microwave source is placed in between a metal plate and small detector between the two. the microwave source is reflected at the metal plate.
The reflector can be moved to and from the source to vary the stationary wave pattern formed, the superposition of the wabe and its reflection produces a stationary wave.
by moving the detector between the transmitter and reflecting plate, you can find the nodes (minima) and antinodes (maxima) of the stationary wave pattern

Question 19

explain how you would demonstrate stationary waves through sound waves

Answer 19

stationary waves are formed inside an air column, which is how insturments such as clarinets and organs work therefore
This can be demonstrated by placing a fine powder inside the air column and a loudspeaker at the open end
At certain frequencies, the powder forms evenly spaced heaps along the tube, showing where there is zero disturbance as a result of the nodes of the stationary wave
to produce a stationary wave there must be a minima (node) at one end and a maxima (antinode) at the end with the loudspeaker

Question 20

what is the distance between each pile of powder (node)

Answer 20

wavelength / 2

Question 21

what is the speed of sound equivalent to?

Answer 21

c = f x lambda therefore c = f x 2d = 2df