Standing Waves

Question 1

Stationary / Standing Waves Setup

Answer 1

A result of two progressive wave with the same amplitude and frequency, travelling at the same speed, but in opposite directions, undergoing superposition producing nodes and antinodes

Usually caused by reflecting a single wave against a reflecting surface to produce a superposition

Question 2

Stationary / Standing Waves Reflecting Setup

Answer 2

The progressive wave is reflected and interfered with incoming (coherent) waves (same frequency, opposite direction)

Question 3

Nodes And Antinodes

Answer 3

When the two waves are exactly equal and opposite, they interfere destructively and produce a node (Displacement is always zero)
When two waves interfere constructively they produce an antinode (Maximum Amplitude)
Nodes are separated by λ/2 (Adjacent)
Antinodes are separated by λ/2 (Adjacent)
Node to Antinode λ/4 (Adjacent)

Question 4

Difference between Progressive and Standing Waves - Progressive

Answer 4

Energy transfer: In the direction of the wave
Wavelength: Distance between two adjacent points in phase
Phase: Changes Across the wave
Amplitude: Same for all (At different times)

Question 5

Difference between Progressive and Standing Waves - Standing

Answer 5

Energy transfer: Is trapped between source and reflector
Wavelength: Nodes separated by λ/2
λ: Wavelength of progressive wave that created the stationary wave
Phase: Points between two nodes are in phase
Either side of a node, particles are in antiphase
Amplitude: Varies from 0 at nodes to maximum at antinodes

Question 6

Standing Waves on a String

Answer 6

String attached between Pulley attached to a weight and a vibrator attached to a frequency generator
Adjust frequency of the generator (from 1st Harmonic) to get different harmonics
On a musical string a standing wave is setup at certain frequencies - These are harmonics, positions of resonance

Question 7

Fundamental Frequency

Answer 7

The lowest frequency that sets up a standing wave
Distance between the two ends of the string at fundamental frequency is λ/2

Question 8

Harmonics

Answer 8

Integer number multiples of the fundamental frequency
Depends on string tension
Mass per unit length (Thicker strings vibrate more slowly - Lower frequencies)
The string length (Shorter strings have shorter vibration wavelengths, leading to higher frequencies)

Question 9

Standing Waves in Pipes

Answer 9

If there is one closed end - Fundamental Frequency is λ / 4: Node at the closed end where reflected
Antinode at the open end
if there is two opened ends - Fundamental Frequency is λ / 2 : Antinodes at each end, and a node in the middle

Question 10

Experiment To determine the Speed of Sound in air

Answer 10

Place a hollow tube into a measuring cylinder of water
Choose a tuning fork and record it’s frequency
Gently tap the tuning fork and hold it just above the hollow tube. The sound waves produced by the fork travel down the tube and get reflected forming a node at the air / water surface
Move the tube up and down until you find the shortest distance between the top of the tube and the water level that the sound form the fork resonates at (when the sound is loudest)
This distance is a quarter of the wavelength of the stationary sound wave
Use v = fλ to find the speed