4.5 Stationary and progressive waves

Question 1

The first harmonic of the string is also known as?

Answer 1

fundamental mode of vibration

Question 2

Define antinode

Answer 2

fixed point in a stationary wave pattern where the amplitude is a maximum

Question 3

What is the distance between adjacent nodes?

Answer 3

Distance between adjacent nodes = 1/2λ

Question 4

Why is there 0 energy at nodes and maximum energy at antinodes?

Answer 4

The amplitude of vibration is 0 at the nodes so there is no energy at the nodes. The amplitude of vibration is a maximum at the antinodes so there is maximum energy at the antinodes.

Question 5

Why does no energy get transferred in a stationary wave?

Answer 5

Because the nodes and antinodes are at fixed positions.

Question 6

What are 2 things that happen in general in any stationary wave pattern?

Answer 6

1. The amplitude of a vibrating particle in a stationary wave pattern varies with position from 0 at a node to maximum amplitude at an antinode
2. The phase difference between 2 vibrating particles is:
   - 0 if the 2 particles are between adjacent nodes or separated by an even number of nodes
   - 180 degrees (π radiants) if the 2 particles are separated by an odd number of nodes.

Question 7

Compare frequency between stationary and progressive waves

Answer 7

S waves : all particles except those at the nodes vibrate at the same frequency

P waves : all particles vibrate at the same frequency

Question 8

Compare amplitude between stationary and progressive waves

Answer 8

S waves : the amplitude varies from 0 at the nodes to a maximum at the antinodes

P waves : the amplitude is the same for all particles

Question 9

Compare phase difference between 2 particles between stationary and progressive waves

Answer 9

S waves : equal to mπ, where m is the number of nodes between the 2 particles

P waves : equal to 2πd/λ, where d= distance apart