Periodic Motion, Waves, and Sound Flashcards Preview

MCAT Physical Sciences > Periodic Motion, Waves, and Sound > Flashcards

Flashcards in Periodic Motion, Waves, and Sound Deck (35):
0

What type of systems exhibit continuous repetitive movement?

Oscillating Systems

1

What are the two characteristics of a linear restoring force?

1. The force is toward the equilibrium position.
2. The magnitude (and acceleration) is proportional to the displacement.

F = -kx
a = -xω^2
ω = (k/m)^1/2

2

Simple Harmonic Motion

An object's oscillation around an equilibrium point due to an elastic linear restoring force. If the path of a particle moving with uniform circular motion were on a line, the particle would oscillate between the points of maximum displacement. Examples are a simple pendulum and a mass-spring.

3

What is the measure of a spring's stiffness and what does it mean if the number is large?

A large spring constant indicates a stiffer spring.

4

Hooke's Law

F = -kx for a mass-spring

5

Angular Frequency

ω = (k/m)^1/2 = 2πf = 2π/T

v = fλ = ω/k = λ/T

6

Period

The number of seconds it takes to complete one cycle. T = 1/f

7

Amplitude

It is the point of maximum displacement.

8

Where do the points of maximum potential and kinetic energy occur in oscillating systems?

At the equilibrium point, potential energy is zero and kinetic energy is at its maximum. At the points of maximum displacement, kinetic energy is zero and potential energy is at its maximum.

9

Where does maximum force occur in an oscillating system?

At maximum displacement

10

Equations for a mass-spring

T = 2π(m/k)^1/2
ω = (k/m)^1/2
KE = 1/2mv^2
U = 1/2kx^2

11

Equations for simple pendulum (θ < 10°)

k = mg/L
T = 2π(L/g)^1/2
ω = (g/L)^1/2
KE = 1/2mv^2
U = mgh

12

Transverse Waves

Like light, where the particles oscillate perpendicular to the direction of motion.

13

Longitudinal Waves

Like sound, the particles oscillate parallel to the direction of motion.

14

Displacement in a wave

y = Y sin(kx - ωt)
k is the wave number = 2π/λ

15

Wavelength

Distance between two equivalent consecutive points on a wave.

16

Frequency

Number of cycles per second (Hz)

17

Phase Difference

Angle that a sine curve leads or lags another, meaning that the waves' crests and troughs occur at different points in time.

18

Node

Point of zero displacement in a standing wave

19

Anti-node

Point of maximum displacement in a standing wave

20

Constructive Interference

In phase overlapping waves' amplitudes add together.

21

Destructive Interference

Out of phase overlapping waves' amplitudes subtract.

22

Wave Speed

v = fλ = ω/k = λ/T

23

Traveling Wave

A propagating wave that reflects and inverts upon reaching it's fixed boundary. The two waves interfere with each other.

24

Standing Waves

Between two fixed nodes only certain wave frequencies can occur. Examples: strings and pipes
λ = 2L/n
Higher harmonics have shorter wavelengths and higher frequencies, but the same wave speed.

25

Resonance

Without external forces, the system oscillates at a natural frequency, where the amplitude will reach its maximum.

Free swinging pendulum: f = (1/2π)(g/L)^1/2 ➡️ only one natural frequency
Mass-spring: f = (1/2π)(k/m)^1/2 ➡️ infinite natural frequencies

26

Forced Oscillation

Application of periodically varying force that is usually small unless close to the natural frequency of the system.

27

How does sound travel?

In a longitudinal wave that causes a mechanical disturbance in a deformable medium, with a relative speed that depends on the particle spacing. It cannot travel through a vacuum and it travels faster through a solid than through a liquid or gas.

In air, at 0°C, sound travels at 331m/s

28

Audible Waves for Humans

20 Hz to 20000 Hz
Below infrasonic
Above ultrasonic

29

Intensity

P = IA
Units: W/m^2

30

Sound Level

β = 10 log (I/Io)
Io = 10^-12 W/m^2

31

Beats

The absolute differences in frequencies of two waves

32

Doppler Effect

f' = f (V +/- VD) / (V +/- VS)
The frequency detected us less than the actual frequency when the source and detector move toward each other. No frequency shift occurs when the source and detector are moving in the same directions at the same speed.

33

Harmonic Series

All the possible frequencies a standing wave can support.

34

Fundamental Frequency

First harmonic of standing waves
f = nv/2L for strings fixed and pipes open at both ends
f = nv/4L for pipes closed at one end (odd integer only)