Interference Pt I

Define Interference

Name two things the amplitude of the resultant wave will depend on

Superposition Principle

If waves interfere constructively, the waves are in ______ with each other (explain). The _______ add causing a _____ _____ _____

If the waves interfere destructively, the waves are exactly _____ _____ _____  with each other (explain). Crest of one wave coincides with the ______ of the other waves and vice versa. Their amplitudes _______, causing a _____ _____ _____

Explain what happens in each of these scenarios. (both 5-story)

a) The pulses have the same ______ but different _______
b) When the pulses overlap, the _____ function is the sum of the individual _____ functions. 
c) When the pulses no longer overlap, they have not been permanently affected by the _______
State which is constructive or destructive 

Assume two waves with the same amplitude, frequency and wavelength, traveling in opposite directions in a medium. State the formula for D_R and D_L 
They interfere according to the _______ _______

Label the standing wave(s) and the traveling wave(s)
Standing wave patterns produced at various times by two waves of equal amplitude traveling in ________ directions 
State the snapshot time (in terms of the period) based on the features of the waves

What is the formula for the resultant wave?
This is the wave function of a _______ ______. There is NO ________ term, and therefore it is NOT a ______ _____

In observing a standing wave, there is no sense of motion in the direction of propagation of either of the ______ _____

D = (2asinkx)cosωt
A node occurs at a point of _____ amplitude at all times, i.e. sinkx = ____ or kx = ____
These correspond to positions of x where 
x = ___, ___, ___, ___,... = ___
where n = ___, ___, ___, ___...

An antinode occurs at a point of ______ ________ (=2a), i.e. sinkx = ____ or kx = ____. What are the corresponding positions of x and n?

Distance between adjacent antinodes is ____. Distance between adjacent nodes is _____.
Distance between a node and an adjacent antinode is ____.

The amplitude of the vertical oscillation of the string depends on the _______ position of the element. Each element ______ within the confines of the envelope function ________. 
Label the diagram

Label the different scenarios
A wave ______ when it encounters a discontinuity.
a) The discontinuity is where the wave speed _______. Which direction will have the faster wave speed?
b) The discontinuity is where the wave speed _______. The reflected pulse is ________

A wave ______ when it encounters a boundary
c) The reflected pulse is _______ and its amplitude is _______

Consider a string fixed at both ends with length L. Standing waves are set up by a continuous ________ of waves incident on and reflected from the ends. There is a boundary condition on the waves

The ends of the strings must necessarily be _____. They are fixed and therefore must have _____ displacement. The boundary condition results in the string having a set of ______ ______ of vibration. Each mode has a characteristic _______.

The normal modes of oscillation for the string can be described by imposing the requirements that the ends be _____. The nodes and antinodes are separated by ____

This is the first normal mode that is consistent with the boundary conditions.
It has ______ at both ends
One ______ is in the middle
This is the _______ wavelength mode
What is the formula for L and λ₁

Consecutive normal modes add an antinode at each step.
The second mode corresponds to λ = ___
The third mode corresponds to λ = ___
In general: λ_n = ____

For standing waves on a string, state the formula for f_n (3)
State the formula for the lowest frequency:
f₁ = ____

The frequencies of the remaining normal modes are integer multiples of the _______ frequency. Frequencies of normal modes that exhibit such an integer multiple relationship form a ______ series, and the normal modes are _______. The fundamental frequency f₁ is the frequency of the first harmonic, the frequency f_n = ____ is the frequency of the nth harmonic, where n is the _______ ________

State the formula for:
f₁ and λ₁
f_n and λ_n (2)
v

Nodes and antinodes are spaced equally.
Each loop (node to node) equivalent to ____
Nodes and antinodes are separated by ____