4.9 Standing Waves

Question 1

When is standing wave formed?

Answer 1

When two identical travelling waves moving in opposite directions meet and superpose.

Question 2

What is important about a standing wave?

Answer 2

Only the amplitude changes, the pattern does not move.

Question 3

What is important about a standing wave on a string?

Answer 3

If the string is fixed at both ends these are nodes on the standing wave.

Question 4

What is the first harmonic?

Answer 4

When the entire string is occupied by one half wave

lambda 1 = 2L

Question 5

What is the second harmonic?

Answer 5

When the entire string is occupied by two half waves

lambda 2 = L

Question 6

What is the third harmonic?

Answer 6

When the entire string is occupied by three half waves

lambda 3 = 2L/3

Question 7

What important about each of these standing waves?

Answer 7

They each have a unique frequency.

Question 8

How can we create a particular harmonic?

Answer 8

Vibrate the string up and down with its associated frequency - creates a travelling wave on the string which upon reflection form the fixed end creates a second travelling wave in the opposite direction.

Question 9

How can a standing wave be set up in open ended pipes?

Answer 9

A traveling wave sent down the pipe will reflect form the ends even though they are open so we have condition for the formation of a standing wave.

Question 10

Where are the nodes and antinodes on a standing wave in open ended pipes?

Answer 10

Molecules at the ends of the pipe vibrate the most so they are antinodes, the molecules in the middle do not oscillator at all so they are a node.

Question 11

What is the first harmonic for open ended pipes?

Answer 11

lamba 1 = 2L

Question 12

What is the second harmonic for open ended pipes?

Answer 12

lambda 2 = L

Question 13

What happens if the pipe has one end closed?

Answer 13

The standing wave will have a node at the closed end and an antinode at the open end.

Question 14

What is the first harmonic for a pipe with one end closed and one end open?

Answer 14

One quarter wavelength filled the pipe

lambda 1 = 4L

Question 15

What is the third harmonic for a pipe with one end closed and one end open?

Answer 15

Three quarter wavelength filled the pipe

lambda 3 = 4L/3

Question 16

What is important about harmonic for pipes where one end is closed?

Answer 16

Only odd number harmonics are possible.

Question 17

What is the difference in energy between standing and travelling waves?

Answer 17

Travelling waves transfer energy, standing waves do not.

Question 18

What is the difference in amplitude between standing and travelling waves?

Answer 18

Travelling waves have constant amplitude, standing waves do not.

Question 19

What are the difference in phase changes between standing and travelling waves?

Answer 19

Different point on a standing wave socialite with different amplitudes. In travelling waves the phase changes as we move along the length of the medium. In standing wave points within two consecutive nodes are in phase. Points within the net pair of node are also in phase but differ by a phase of Pi from the first set of points.