Module 4 - Section 2 - Stationary Waves

Question 1

When do you get a stationary wave ?

Answer 1

When a progressive wave is reflected at a boundary

Question 2

What is a stationary wave ?

Answer 2

A stationary wave is the superposition of two progressive waves with the same wavelength - moving in opposite directions - for e.g. of you have a rope and make waves at one end and your friend is holding the rope on the other end and making waves then there are two waves which are going opposite directions and this creates a stationary wave

Question 3

Whats the difference between a progressive wave and a standing wave ?

Answer 3

Unlike progressive waves - no energy it’s transmitted by a stationary wave

Question 4

How can you demonstrate a stationary wave ?

Answer 4

You can demonstrate a standing wave by attaching a vibration transducer to a stretched rope with one end fixed and then you would attach a signal generator to the vibration transducer and this creates a wave by vibrating the rope ( string ) - the wave generator by the transducer is reflected back and forth by the fixed end of the string - you have to change the frequency of the generator to a resonance frequency and this is where you get a stationary wave where the pattern doesn’t move and just goes up and down as for other frequencies you wouldn’t get this and it would be a jumble

Question 5

What is a resonant frequency ?

Answer 5

It is the frequency at which the stationary wave pattern doesn’t move and it just goes up and down

Question 6

How can you find the resonant frequency ?

Answer 6

You have to find how long it takes for a single wave to get to the end and back - and then use this to find how much waves should be generated - if it takes a wave 2 secs to get there and back then the generator should be set at 2 waves - the transducer should produce the exact amount of waves in the time that it takes one wave to get there and back - as the original and the reflected wave reinforce each other and make a pattern

Question 7

What do stationary waves in strings form ?

Answer 7

They form oscillating loops which are separated by nodes

Question 8

Whats a node ?

Answer 8

It’s where the amplitude of the vibration is zero

Question 9

What are antinodes ?

Answer 9

They are the points of maximum displacement

Question 10

What happens at resonant frequencies ?

Answer 10

At resonant frequencies - an exact number of half wavelengths fits onto the string - this is because at resonant frequencies there are loops and each loop is half a wavelength and you can’t get half a loop so there will always be an exact number of half wavelengths on the string for example if there are 2 loops then there will be 2 half wavelengths so the amount of half wavelengths is exact

Question 11

Whats the lowest possible resonant frequency called ?

Answer 11

It’s called the first harmonic - it has one loop which is half a wavelength and it has 2 nodes - one at each end

Question 12

Whats another name for the first harmonic ?

Answer 12

The fundamental mode of vibration

Question 13

What does the second harmonic consist of ?

Answer 13

It is twice the fundamental mode of vibration

It has 3 nodes - on in the middle and one on each end of the string

It has two loops

Question 14

What does the third harmonic look like ?

Answer 14

The third harmonic is 3x the fundamental mode of vibration - it has 4 nodes - 3 loops and it has 1 1/2 wavelengths or 3 half wavelengths

Question 15

What type of wave do stringed instruments make ?

Answer 15

Transverse stationary waves

You finger sets the string vibrating and waves are sent in both directions and are reflected back at both ends

Question 16

What wave do wind instruments make ?

Answer 16

Wind instruments make longitudinal standing waves

Question 17

What happens to the stationary wave if the instrument has a close end ?

Answer 17

A node will form at the closed end

Question 18

When do you get the lowest resonant frequency in a closed tube

Answer 18

You get the lowest resonant frequency - when the length ( l ) of the pipe is a quarter wavelength landa/4

This is because when sound gets reflected at a closed end a node forms and then at the opening part of a tube a antinode forms and the distance between a node and a antinode is a quarter of a wavelength so you get the lowest resonant frequency when the length of a pipe is a quarter wavelength

Question 19

Where do anti-nodes form on wind instruments ?

Answer 19

Antinodes form at the open ends of the instrument

Question 20

How do you get the lowest resonant frequency if both ends of the tube are open ?

Answer 20

if both ends are open then you get the lowest resonant frequency when the length (l) of the pipe is a half wavelength

Question 21

How can you demonstrate a stationary wave with microwaves ?

Answer 21

1) microwaves are produced with a microwave transmitter and then the waves are reflected of a metal plate back towards the transmitter - the reflected and incoming waves interfere and set up stationary waves

2) you can then find the nodes by moving the microwave receiver between the transmitter and the reflecting plate - whenever a node is detected - the receiver will read a minimum value and then if you keep on moving the receiver and it detects a antinode - it will read a maximum

Question 22

How can you measure the speed of sound with stationary waves ?

Answer 22

1) Firstly you can create a closed-end pipe by placing a hollow plastic tube into a measuring cylinder which is filled with water

2) then get a tuning fork and note down its frequency as we need this for our wave equation to find out the speed of sound - so we just have to find the wavelength of the stationary wave

3) Then hit the tuning fork and place it over the tube and then move the tube up and down until you can hear the fundamental note - when this happens the progressive sound waves from the fork are reflected of the water surface and a node is formed there and then a antinode is formed at the opening of the tube

4) Once the fundamental note is heard - you then have to measure the length of the glass tube at which the stationary wave it set up at - from the surface of the water to the opening of the tube - then we know that the length of the tube is 1/4 of a wavelength as its a closed tube so therefore the length = landa / 4 so then we can rearrange to get wavelength = 4 x length
So our measuring of the tube get x by 4 and this gives us a wavelength then plug the freq and this value to the wave speed equation to get the speed of sound

We can also make the practical more reliable by raising the tube up again until we hear the fundamental note again and then we know that its the second harmonic so we get a 2 nodes and 2 antinodes which is 3/4 of a wavelength and then we get an average etc etc

Question 23

Whats the difference of amplitude between a standing wave and a progressive wave ?

Answer 23

When a string forms a standing wave - the amplitude varies from a maximum at the antinode to zero at the node - with progressive waves the amplitude has the same value everywhere