C.4 Standing Waves and Resonance Flashcards
When do standing waves occur?
When two waves of the same type meet, with the same amplitude, frequency and travel in opposite directions
For a string fixed at both ends, when will a standing wave occur?
If the wavelength fits the string
First harmonic wave
Lowest frequency at which a standing wave will form
First harmonic wave frequency and length
L = λ/2 so λ = 2L
f = fo (lowest frequency)
Second harmonic frequency and length
L = λ
f = 2fo
Third harmonic frequency and length
L= 3 λ/2
f = 3fo
Resonance
When a system oscillates at its natural frequency and the amplitude increases
When a wave is forced to oscillate at a frequency that is not its resonance
Forced osciallation
Damping
The dissipation of energy from an oscillator due to resistive forces
Light damping
Light continues to oscillate taking a relatively long time to return to it’s equilibrium position.
Light damping amplitude and frequency
Amplitude decreases with an exponential decay and the frequency is unchanged
Heavy damping
No oscillations but takes a long time to return to equilibrium
Critical damping
No oscillations but takes a short time to return to its equilibrium position
Damping and natural frequency
Damping will slightly reduce the natural frequency of a system and significantly reduces the amplitude of the oscillation
Standing wave in a pipe
It will only form if the wavelength fits the pipe
