How frequency and wavelength vary in stationary waves
Fig. 16.25 shows a stationary wave set up between two fixed points, with nodes (N) and antinodes (A). These diagrams illustrate the relationship of internode distance (distance between nodes and/or antinodes) to the fraction of wavelength present.
Antinode: This is the maximum displacement of the wave from its base level. Note the following from Fig. 16.25.
• Node: This is the minimum displacement of the wave from its base level. •
NOTE
Remember that a wavelength is the distance from a point on a wave to its corresponding point.
• The fixed points at either end are always nodes.
• There are two antinodes in every wavelength.
• There are three nodes in every wavelength.
• The distance between consecutive nodes is half
a wavelength 2 l ) .
( 1 __
• The distance between consecutive antinodes is half
a wavelength 2 l ) .
( 1 __
• The distance between a node and the next antinode is a quarter of a wavelength
( 1 __
4 l ) . QUESTIONS AND ANSWERS
4. If water on a rope has a frequency of 25 Hz and travels at 2.5 m s−1, calculate the distance between its consecutive nodes.
Solution c = f λ ⇒ 2.5 = (25)(λ), so λ = 2.5
__ 2 λ
_____ 25 = 0.1 m
Distance between consecutive nodes = 1
= 0.05 m
5. A tuning fork is used to vibrate a stretched string with sound waves travelling at 335 m s–1. If the distance between adjacent nodes is 1.4 m, determine the frequency of the wave.
Solution
1.4 m between consecutive nodes means λ = 2.8 m
c = f λ ⇒ 335 = (f )(2.8)
so f = 335 You may now complete Exercise 16B (page 186).
_____ 2.8 = 119.64 Hz
N NN N A AA A
FIG. 16.25 A stationary wave set up between two fixed points
