3.2 Stationary Waves

Question 1

How are stationary waves produced?

Answer 1

by the superposition of 2 waves of the same frequency and amplitude travelling in opposite directions

Question 2

What are the properties of progressive waves?

Answer 2

• all points have the same amplitude
• points exactly a wavelength apart are in phase
• the phase of points within one wavelength can be between 0 and 360 degrees
• energy is transferred along the wave
• has no nodes or antinodes
• the wave speed is the speed at which the wave moves through a medium

Question 3

What are the properties of stationary waves?

Answer 3

• each point has a different amplitude depending on the amount of superposition
• points between nodes are in phase and either side are out of phase
• energy is stored and not transferred
• has nodes and anti nodes
• each point on the wave oscillates at a different speed. the overall wave does not move

Question 4

What are nodes?

Answer 4

• a region of a stationary wave with no vibrations
• nodes are fixed

Question 5

What are anti nodes?

Answer 5

• a region of stationary waves where the vibrations are at their maximum amplitude
• anti nodes only move in the vertical direction

Question 6

What is the relationship between phase difference and nodes/antinodes?

Answer 6

• 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 7

What is the principle of superposition?

Answer 7

• when two or more waves with the same frequency arrive at a point, the resultant displacement is the sum of the displacements of each wave

Question 8

How do 2 waves superpose with each other in phase?

Answer 8

• causing constructive interference.
• peaks and troughs line up on both waves and the resultant wave has double the amplitude

Question 9

How do 2 waves superpose each other in anti-phase?

Answer 9

• causes destructive interference
• the peaks on one wave line up with the troughs of the other
• resultant wave has no amplitude

Question 10

What waves does the principle of superposition apply to?

Answer 10

all types of waves

Question 11

When is a stationary wave formed?

Answer 11

two waves travelling in opposite directions along the same line with the same frequency superpose

Question 12

what most occur for a stationary wave to be formed?

Answer 12

• the same wavelength
• a similar amplitude

Question 13

What occurs at the nodes of a stationary wave?

Answer 13

• the waves are in anti-phase meaning destructive interference occurs
• causing the 2 waves to cancel each other out

Question 14

What occurs at the anti node of a stationary wave?

Answer 14

• out of phase thus constructive interference occurs
• causes the waves to add together

Question 15

What are 3 examples of stationary waves?

Answer 15

• stretched string
• microwaves
• sound waves

Question 16

How can a stretched string be an example of a stationary wave?

Answer 16

• vibrations caused by stationary string produce sound e.g. violin
• at specific frequencies known as resonant frequencies a whole number of has wavelengths will fit on the length of string
• as the resonant frequencies of the oscillator are achieved standing waves with different numbers of minima and maxima form

Question 17

How do microwaves work as stationary waves?

Answer 17

• placed in line with a reflecting plate and a small detector between the two
• the reflector can be moved to and from the source to vary the stationary wave pattern formed
• by moving the detector it can pick up the maxima and minima

Question 18

How do sound waves work as stationary waves?

Answer 18

• produced as a result of the formation of stationary waves inside an air column
• at one end of the speaker a minima is present and the other a maxima

Question 19

What are harmonics

Answer 19

the different wave patters
- dependent on frequencies of the vibration and situation they’re created
- can be observed on a string with 2 fixed ends
- as the frequency increased more harmonics begin to appear

Question 20

How do harmonics work on a string?

Answer 20

• the wave is fixed at both ends
• the simplest wave patter is a single loop made up of 2 nodes and an antinode

Question 21

What is the fundamental frequency?

Answer 21

• when a stationary wave like a vibrating string is fixed at both ends,
• the simplest wave pattern is a single loop made up of two nodes and an antinode

Question 22

What is the particular frequency of stationary waves dependent on?

Answer 22

• length of the string
• wave speed

Question 23

What is the second harmonic?

Answer 23

• a stationary wave with 3 nodes and 2 antinodes

Question 24

What is the 3rd harmon?

Answer 24

• 4 nodes and 3 antinodes

Question 25

What is the relationship between the nth harmonic and nodes?

Answer 25

nth harmonic has n antinodes and n+1 nodes

Question 26

What are the wavelength and frequencies the first harmonic?

Answer 26

wavelength = 2L
f = v/2L

Question 27

What is the wavelength and frequency of the second harmonic?

Answer 27

wavelength = L
f=v/L

Question 28

What is the wavelength and frequency of the third harmonic?

Answer 28

wavelength = 2L/3
f=3v/2L

Question 29

What is the relationship between frequency and n?

Answer 29

nth harmonic the frequency = n x frequency of first harmonic