9. Waves Flashcards
What is the difference between period and frequency?
Period (T) = the number of seconds per cycle
frequency (f) = the number of cycles per second, measured in Hertz
T = 1 / f f = 1 / T
What is Hooke’s law of springs?
An object in harmonic motion is being moved by the force of the oscillating spring.
F = -kx
k = spring constant, specific for a given spring x = displacement from equilibrium (x=0)
Why is Hooke’s law a negative force?
The force always opposes the direction of displacement. This is known as a restoring force.
When we initiate the oscillations of a spring, we pull the spring out over some distance meaning we are doing work. When work is being done against the spring, the spring must store potential energy. What is elastic potential energy?
PE = 1/2kx^2
k = spring constant x = displacement from equilibrium (x=0)
This is similar to 1/2mv^2 and 1/2ρv^2 (except these are for KE)
t or f, work done by the spring = -ΔPE elastic
true
Assuming no friction, what is true of total mechanical energy for an oscillating spring?
If no friction is considered, then PE + KE = 0. Total mechanical energy will be conserved.
1/2kx^2 + 1/2mv^2 = 0
How can you find the maximum speed of an object oscillating on a spring?
At max speed, all PE is converted to KE.
PE max = KE max
1/2kA^2 = 1/2mv^2
kA^2 / m = v^2
v max = A x (k / m)^1/2
Unlike a spring, the restoring force of a pendulum is gravity acting on the object in motion. How do you calculate this?
F = mgsinϴ
ϴ is the angle between the vertical (an extended line from the string holding the object) and the mg (directly downwards)
How does mass affect the period and frequency of an object oscillating on a pendulum?
Mass has NO effect on period or frequency.
These are only effected by the length of oscillation
What is the wave equation for speed of a wave?
v = f x λ
What are the two big rules for waves? (hint: wave speed, changing mediums)
- Although v = f x λ, the speed of a wave does NOT depend on frequency or wavelength. It depends only on the characteristics of the medium it travels in. Thus, if increase a waves frequency (e.g. rope) then wavelength must go down since velocity is constant for that medium.
- When a wave changes its medium, its speed changed (since medium determines wave speed) buts is frequency DOES NOT change. Thus, wavelength must change accordingly.
What determines the amplitude of a wave?
The amount of energy going through it. Note that amplitude is unaffected by frequency and wavelength.
What is constructive and destructive wave interference?
constructive - crest meets crest (in-phase) and resulting wave amplitude increases
destructive - waves are out of phase and resulting wave amplitude decreases
What is a standing wave?
A standing wave is a special kind of wave in which the horizontal positions of the medium remain permanently fixed (e.g. you pulse a rope which is attached to a wall).
If you pulse the rope at the correct frequency, the waves interfere in a way where they stand still (standing wave).
Areas of the wave which do not vibrate up and down at all are called nodes (no displacement)
What is the distance between 2 nodes of a standing wave?
the distance between two nodes is half the wavelength.
thus, a 3 node standing waves full distance (distance between horizontal fixed positions) is exactly equal to its wavelength.
