Waves and Periodic Motion

Question 1

Visual Representation of Amplitude and Period

Question 2

Amplitude, Period, and Frequency

Answer 2

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

Question 3

Angular Frequency

Answer 3

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

w = 2πf

Question 4

In-Phase Graph

Answer 4

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

Question 5

Out of Phase Graph

Answer 5

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

Question 6

Hooke’s Law

Answer 6

F= -kx

Question 7

Constants of Hooke’s Law

Answer 7

constant = PEmax = ½kA²

constant = KEmax = ½mv² at x = 0

Question 8

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

Answer 8

At the maximum displacement (amplitude)

Question 9

When is kinetic energy at its maximum?

Answer 9

At the equilibrium position x = 0

Question 10

Simple harmonic motion; displacement as a sinusoidal function of time

Answer 10

x = A·sin(wt)

x is displacement.

A is amplitude.

w is angular frequency (also called angular velocity).

t is time.

Question 11

Motion of a spring with mass attached to its end

Answer 11

and

Question 12

The spring vibrates faster if…

Answer 12

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

Question 13

Motion of a pendulum

Answer 13

and

Question 14

The pendulum oscillates faster when…

Answer 14

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

Question 15

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

Answer 15

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.

Question 16

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

Answer 16

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.

Question 17

Transverse Wave

Answer 17

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

Question 18

Longitudinal Wave

Answer 18

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

Question 19

Standing Wave

Answer 19

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.

Question 20

Wavelength, frequency, velocity

Answer 20

v = fλ

Question 21

Amplitude, intensity

Answer 21

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.

Question 22

Does a larger amplitude indicate a higher energy photon?

Answer 22

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.

Question 23

Constructive Interference

Answer 23

Constructive interference: addition of waves resulting in greater amplitude.

Question 24

Destructive Interference

Answer 24

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

Question 25

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

Answer 25

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

Question 26

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

Answer 26

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

Question 27

Resonance

Answer 27

Resonance is when things oscillate at its maximum amplitude.

Question 28

Constructive and Destructive Inteference in Ripple Waves

Question 29

Open ended string length

Answer 29

L = (n/2)λ

Question 30

Closed string length

Answer 30

L = (n_odd/4)λ

Question 31

Node and Antinode

Answer 31

Node: point where there’s no oscillation.

Antinode: point where there’s maximum oscillation.

Question 32

Beat Frequencies

Answer 32

Beats occur when two waves coexist at different frequencies.

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

Question 33

Refraction

Answer 33

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

Question 34

Diffraction

Answer 34

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