3.3.1.3 Waves: Principle of superposition of waves and formation of stationary waves Flashcards
What is the principle of superposition?
When two or more waves cross, the resultant displacement equals the vector sum of individual displacement.
What is constructive interference?
When two waves meet, if their displacements are in the same direction, they combine to give a bigger displacement. - they arrive at a point in phase with each other
What is destructive interference?
When a wave with positive displacement and a wave with negative displacement meet they will cancel each other out. - they arrive at a point in anti-phase
What is total destructive interference?
When two waves with equal and opposite displacements meet and cancel each other out completely
What is a stationary wave?
The superposition of two progressive waves with the same frequency (or wavelength) and amplitude moving in opposite, directions.
What is the feature of stationary waves?
No energy is transmitted
What are resonant frequencies?
The frequencies at which stationary waves are formed - the oscillator produces an exact number of waves in the time it takes for a wave to get to the end and back again, then the original and reflected waves reinforce each other.
(an exact number of half wavelengths fit onto a string)
(the frequency at which a stationary wave is formed because an exact number of waves are produced in the time it takes for a wave to get to the end of the string and back again)
What is a node on a stationary wave?
A point where the amplitude is zero
- total destructive interference
What is an antinode on a stationary wave?
A point of maximum amplitude
- constructive interference
What is the first harmonic?
The lowest possible resonant frequency, has one antinode and 2 nodes. The stationary wave produced has a half wavelength
What is the second harmonic?
Twice the frequency of the first harmonic, produces a stationary wave of 2 half wavelengths
What are the factors affecting resonant frequency?
String length - longer string = lower resonant frequency because half-wavelength is longer.
String mass - heavier = lower resonant frequency because waves travel more slowly down the string.
Tension - lower tension = lower resonant frequency, waves travel more slowly in a loose string.
What is the formula for resonant frequency?
f = (1/2l) sqrt(T/mu)
mu (mass per unit length) = Mass of string/length of string
T (tension) = m (total mass of MASSES) * g (acceleration due to gravity)
