C.4 Standing waves and resonance Flashcards
Standing wave
Formed by the superposition of two waves traveling in opposite directions, with the same amplitude, resulting in a wave that appears to stand still.
Nodes in a standing wave
Ppoints along a standing wave where there is zero amplitude due to destructive interference, resulting in no motion at these points
Antinodes in a standing wave
Points of maximum displacement along a standing wave, where constructive interference occurs, resulting in the highest amplitude
What causes the formation of standing waves?
Standing waves are formed by the interference of two waves of the same frequency and amplitude traveling in opposite directions.
How does the phase difference between nodes and antinodes in a standing wave manifest?
In a standing wave, nodes and antinodes exhibit a phase difference of 180 degrees, with nodes being points of complete destructive interference and antinodes points of constructive interference
What boundary condition causes a node at the end of a string?
A fixed boundary, where the string is held stationary, causing zero amplitude at that point.
What is the first harmonic in a string fixed at both ends?
The simplest standing wave pattern with two nodes and one antinode, representing the longest possible wavelength.
How do harmonics in open pipes differ from those in closed pipes?
Open pipes can support all harmonics, including even and odd, while closed pipes only support odd harmonics (1st, 3rd, 5th, etc.).
What does an antinode at a pipe’s end indicate about its boundary condition?
An open end, allowing maximum amplitude oscillation of air particles.
How is the wavelength related to the length of the string or pipe for the first harmonic?
The wavelength is twice the length of the string or pipe for the first harmonic in both strings and open pipes.
Resonance
The phenomenon where an oscillating system experiences maximum amplitude when the driving frequency matches its natural frequency.
What causes damping in an oscillating system?
The presence of resistive forces like friction or air resistance, leading to the gradual loss of energy in the system
What is the effect of light damping on an oscillator?
The system continues to oscillate with a gradually decreasing amplitude over time.
What distinguishes critical damping in a system?
The system returns to its equilibrium state as quickly as possible without oscillating.
How does heavy damping affect an oscillating system?
The system gradually loses all its energy and returns very slowly to its equilibrium state without oscillating.
