Visual Representation of Amplitude and Period

Amplitude, Period, and Frequency

**Amplitude (A)**: how high the peaks are or how low the troughs are, in meters.

**Period (T)**: the time it takes for one cycle, in seconds.

T = 1/f

**Frequency (f)**: the rate, or how many cycles per second, in Hertz (cycles per second).

f = 1/T

Angular Frequency

Angular frequency (w): the rate, in how many radians per second.

w = 2πf

In-Phase Graph

In phase: the waves are 0 or 2π radians (0 or 360°) apart. The resulting amplitude (sum of the waves) is twice the original.

Out of Phase Graph

### Out of phase: resulting amplitude is between 0 and twice the original.

Hooke's Law

F= -kx

Constants of Hooke's Law

constant = PEmax = ½kA^{2}

constant = KEmax = ½mv^{2} at x = 0

When is potential energy at its maximum in Hooke's Law?

At the maximum displacement (amplitude)

When is kinetic energy at its maximum?

At the equilibrium position x = 0

Simple harmonic motion; displacement as a sinusoidal function of time

x = A·sin(wt)

x is displacement.

A is amplitude.

w is angular frequency (also called angular velocity).

t is time.

Motion of a spring with mass attached to its end

and

The spring vibrates faster if...

The spring vibrates faster if it's stiffer and if the mass attached to it is smaller.

Motion of a pendulum

and

The pendulum oscillates faster when...

The pendulum oscillates faster when gravity is large and when the string is short.

If you are given the velocity at the equilibrium position, then you should be able to find out the amplitude by...

If you are given the velocity at the equilibrium position, then you should be able to find out the amplitude by setting maximum KE = maximum PE.

If you are given the amplitude, then you should be able to find out the velocity at the equilibrium position by...

If you are given the amplitude, then you should be able to find out the velocity at the equilibrium position by setting maximum PE = maximum KE.

Transverse Wave

Transverse wave: wave displacement is perpendicular to the direction of motion. Examples include light.

Longitudinal Wave

Longitudinal wave: wave displacement is parallel to the direction of motion.

Standing Wave

A standing wave by oscillating a string side ways. The speed for such a wave = square root of (string tension / mass per unit length of the string). For the MCAT, just know that tense, light strings can produce faster transverse waves.

Wavelength, frequency, velocity

v = fλ

Amplitude, intensity

Amplitude is correlated with the energy of the wave.

Greater amplitude = greater energy of the wave.

Intensity = energy per area per time = power per area.

Thus, amplitude and intensity are correlated.

Greater amplitude leads to higher intensity.

Does a larger amplitude indicate a higher energy photon?

amplitude and intensity increases the overall energy of electromagnetic waves such as light. However, neither amplitude nor intensity changes the energy per photon. Energy per photon depends on wavelength. The shorter the wavelength (also the higher the frequency), the greater the energy.

Constructive Interference

Constructive interference: addition of waves resulting in greater amplitude.

Destructive Interference

Destructive interference: addition (cancellation) of waves resulting in diminished amplitude.

When in-phase waves add, what happens to the amplitude?

When in phase waves add, the resulting wave has a greater amplitude.

When out of phase waves add, what happens to the amplitude?

When out of phase waves add, the resulting wave has a smaller amplitude.

Resonance

Resonance is when things oscillate at its maximum amplitude.

Constructive and Destructive Inteference in Ripple Waves

Open ended string length

L = (n/2)λ

Closed string length

L = (n_{odd}/4)λ

Node and Antinode

Node: point where there's no oscillation.

Antinode: point where there's maximum oscillation.

Beat Frequencies

Beats occur when two waves coexist at different frequencies.

The beat frequency is the difference between the frequencies of the two waves.

Refraction

Refraction is the bending of waves when it meets a boundary between one medium to another.

Diffraction

Diffraction is the spreading (diffusion) of waves around edges of apertures and obstacles.