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