WAVES

Representing Waves Graphically
 
Students should be able to:

• Explain qualitatively why disturbing a continuous system from equilibrium results in a wave.
• Describe the difference between a transverse wave and a longitudinal wave.
• Draw both history and snapshot graphs of one dimensional waves.
• Given a history graph, draw a snapshot graph, and vise versa.
• Given a displacement graph for a longitudinal, draw a representation of the longitudinal displacements.

 
Students should be able to:

• Describe what the displacement function D(x,t) represents.
• Describe the form of D(x,t) for left and right  moving pulses
• Predict whether or not a wave pulse on a string will be inverted upon reflection (given a fixed or free end).
• Explain what the Superposition Principle tells us, and use this to predict the displacement function for pulses passing though each other.

Sinusoidal Waves
 
Students should be able to:

• Explain what a sinusoidal wave is.
• Determine the speed of a sinusoidal wave given the snapshot and history graphs of a sinusoidal wave.
• Determine the wavelength and frequency of a sinusoudal wave given D(x,t).
• Calculate the speed of a sinusoidal wave given D(x,t).
• State the relationship between wavelength, frequency, and velocity, and explain how to derive this.

Index of Refraction
 
Students should be able to:

• Determine the wavelength, frequency, and velocity of a light wave in a medium with some given index of refraction, if the wavelength/frequency for the wave outside the medium are given
• Explain why the frequency of a wave is the same everywhere.

Superposition
 
Students should be able to:

• Plot subsequent snap shot graphs of two pulses travelling towards each other and interfering with each other.
• Determine if a point at a distance from two sources is interfering constructively or deconstructively.
• Calcualte the locations at which destructive interference (or constructive interfernce) will occur from two sources.
• Explain qualitatively why we get an interference pattern from a double slit apparatus.

Standing Waves
 
Students should be able to:

• Use superposition to explain how a standing wave is created.
• Draw the fundamentals and harmonics of fixed-fixed (closed-closed), fixed-free (closed-open), and free-free (open-open) systems.
• Apply the theory of standing waves to wind intruments and stringed instruments (i.e., determine frequency, harmonics, string tension, linear density, speed of sound, length etc...)