Wave Properties
Wavelength
Longitudinal (pressure waves)
When preparing a graph of density vs time for an individual particle experiencing a disturbance from a longitudinal wave, what information can be directly obtain from an analysis of the graph?
Period- (duration of time required for the individual particle to complete a single cycle).
Draw the fundamental frequency for a standing wave in closed pipe and also for an open pipe.
Closed Pipe: L = 1/4 λ
Open Pipe: L = 1/2 λ
Consider an electromagnetic wave traveling through the vacuum of space and far away from any significant forces. How would the speed of electromagnetic radiation be influenced by doubling the wavelength?
Speed of light in a vacuum is constant. If wavelength is doubled, then frequency is halved to keep the speed of light constant. All forms of electromagnetic radiation travel at a constant speed in a vacuum far removed from any gravitational forces.
Frequency
Light can be considered to produce waves of this type.
Transverse
Prepare a plot of the potential, kinetic and total energies for an individual particle on a rope, fixed at both ends and oscillating at the rope's fundamental frequency. Include three complete cycles in your graph.
See png image.
A sound wave (traveling at 343 m/s) resonates inside a pipe open at both ends producing a standing waveform of the second harmonic. Determine the length of the pipe if the frequency of the wave is 420 Hz.
v = f λ
2nd Harmonic for an open pipe: L = λ
Answer: L = λ = 0.82 m
Which factors influence the speed of a pulse sent along a string fixed on one end?
Tension (force) and mass of the string. Greater tensions produce faster waves. Lower masses produce faster waves.
Period
Transverse waves
What type of waveform (wavefunction) results from preparing a plot of an individual particle's position with respect to time for a particle on a rope fixed at both ends and driven at its 2nd harmonic.
Sine or cosine
Nodes: No arrows
Anti-nodes: Largest arrows
L = 3/4 λ
E = hf and c = fλ so f =c/λ
therefore, E=(h) (c/λ)
Frequency and wavelength
(v = f•λ)
The displacement of particles in the medium is parallel to the propagation of the wave.
Longitudinal (pressure waves)
What specific information can be determined from analyzing the displacement along the y-axis (Δy) vs the position along the x-axis for a transverse wave at an instantaneous moment?
Open Pipe: L = 1/2λ
Closed Pipe: L = 1/4 λ
Frequency (pitch) is 2x's lower in closed pipe.
How will a reflected pulse sent along the length of a string fixed on one end be changed compared to the incident pulse?
Reflected, inverted, equivalent amplitude (assuming no dissipation of energy)
How does varying the amplitude of a wave producing blue light affect what the observer would see?
Varying the amplitude of a transverse, visible light wave will directly increase the intensity of light (greater amplitude) or decrease the intensity of light (smaller amplitude).
Ocean waves and seismic waves produced during an earthquake can be considered to produce what type(s) of waves?
Both transverse and longitudinal
Provide a plot of a particle's position for a spring suspended vertically from the ceiling that undergoes simple harmonic motion.
Sine/Cosine wave function
Consider the fundamental frequency of a standing sound wave resonating in a pipe closed at one end. How much longer would the pipe need to be in order to be the same length as the wavelength of fundamental frequency (1st harmonic)?
Closed pipe: L = 1/4 λ so;
4L = λ (i.e. four times longer than the current length of the pipe)
Nodes and antinodes remain in the same positions.
Amplitudes (crest and troughs) are displaced to a greater extent (become higher and lower) from equilibrium.