Wave properties 3

Question 1

What is the simplest stationary wave?

Answer 1

The first harmonic of the string/fundamental mode of vibration

Question 2

What does the first harmonic consist of?

Answer 2

• Single loop that has a node at either end.

* String vibrates with maximum amplitude midway between the nodes, this is the anti node

Question 3

What is the anti node?

Answer 3

Position of maximum amplitude

Question 4

What is the distance between adjacent nodes/

Answer 4

• Distance between adjacent nodes = 1/2 x wavelength

* Applies to first harmonic

Question 5

What do stationary waves in strings form?

Answer 5

• Stationary waves in strings form oscillating loops separated by nodes
• Each particle vibrates at right angles to the string

Question 6

What are nodes?

Answer 6

Areas where the amplitude of the vibration is zero

Question 7

What are antinodes?

Answer 7

Points of maximum amplitude

Question 8

What is the number of wavelengths at resonant frequencies?

Answer 8

At resonant frequencies an exact number of half wavelengths fits onto the string

Question 9

What is the second harmonic?

Answer 9

• Twice the frequency of the first harmonic

* Two loops with a node in the middle, and one at each end

Question 10

What is the third harmonic?

Answer 10

• Three times the frequency of the first harmonic

* 1 1/2 wavelength fits on the string

Question 11

What is a stationary wave?

Answer 11

The superposition of two progressive waves with the same frequency ( wavelength ) moving in opposite directions.

Question 12

What energy do stationary waves emit?

Answer 12

• Stationary waves that vibrate freely do not transfer energy to their surroundings.
• No energy is transmitted by a stationary wave.

Question 13

What is the energy at nodes?

Answer 13

• Amplitude is zero at nodes

* There is no energy at the nodes

Question 14

What is the energy at anti nodes?

Answer 14

• Amplitude of the vibration is at a maximum at the anti nodes
• There is a maximum energy at the anti nodes

Question 15

What happens when stationary waves are in phase?

Answer 15

They reinforce each other to produce a large wave

Question 16

How does the amplitude of a vibrating particle vary in a stationary wave?

Answer 16

Varies with position from zero at node to maximum at the anti node

Question 17

What is the phase difference between two vibrating particles in a stationary wave?

Answer 17

• Zero if two particles are between adjacent nodes or separated by an even number of nodes
• 180 degrees if the two particles by an odd number of nodes

Question 18

What is the frequency of particles in progressive waves?

Answer 18

All particles vibrate at the same frequency

Question 19

What is the frequency of particles in stationary waves?

Answer 19

• All particles except those at the nodes vibrate at the same frequency

Question 20

What is the amplitude of stationary waves?

Answer 20

• Amplitude varies from zero at the nodes to a maximum at the anti nodes

Question 21

What is the amplitude of progressive waves?

Answer 21

Amplitude is the same for all particles

Question 22

What is the phase difference between two particles in stationary waves?

Answer 22

• Equal to m x pi

* Where m is the number of nodes between two particles

Question 23

What is the phase difference between two particles in progressive waves?

Answer 23

• Equal to 2 pi x d / wavelength

* Where d = distance apart, lambda is the wavelength

Question 24

What are some stationary waves in a pipe?

Answer 24

• Sound resonates at certain frequencies in an air filled tube or pipe
• In a pipe closed at one end, these resonant frequencies occur when there is an anti node at the open end and a node at the other end