Final Exam, Thursday May 4th 8 pm,

Room TBA

25 Multiple choice questions

~17 from material since Test 3Chapter 11 (except section 11.3 and 11.6):

• Heat, specific heat, latent heat

Chapter 13 (all of it)

• Hooke’s law, spring potential energy, SHM,

pendulum, waves

Chapter 14 (through section 14.5)

• Sound waves, speed of sound, intensity of sound,

spherical waves

• Heating an object-specific heat

– Different slopes since cwater > cice

Time

Tem

per

ature

ice

water

steam

Melting Point

Boiling Point

Q = m c ∆T

Changing phase-latent heat

Q = ±m L

Applying constant heat per second

mLv

mLf

Lf<Lv

Transferring heat energy

• 3 mechanisms

– Conduction

• Heat transfer through material

– Convection

• Heat transfer by movement of hot material

– Radiation

• Heat transfer by light

Hooke’s Law (Restoring Force)

FS = -kx (Hooke’s Law)

k is the spring constant (N/m)

Spring Potential Energy

(x)

Fs= slope=k

ersonpring

pring

erson

2

21 kxPES

Energy in an oscillator

• Total energy of system (no frictional forces

doing work):2

212

21 kxmvPEKEE

• E is the same everywhere - as KE increases

PE decreases and vice-versa

• E in terms of amplitude: when x = A, v = 0

2

21 kAE

• The period is the time for one oscillation

• The frequency gives the number of cycles per second

• The angular velocity/speed (or angular frequency)gives the number of radians per second

m

kƒ2

m

k

2

1

T

1ƒ

k

m2T

tAx cos

tAv sin

tAa cos2

m

kAa max

Note: v is slope of x vs. t

a is slope of v vs. t

m

kf 2

Pendulum = Simple Harmonic Motion

xL

mgFpendulum

Effective “spring constant” is keff = mg/L

g

LTpendulum 2

bob

Period of simple pendulum is independent of mass or amplitude;

instead depends on the length of cord

Transverse

Longitudinal

Mechanical Wave Definitions

Amplitude: maximum height of crest or depth of trough (not both!)

Wavelength (l): distance over which wave repeats itself

Frequency (f): Number of crests that pass a given point per unit time

Wave velocity: a crest travels one wavelength in one period T:

Tv

l fl

Waves on Strings

fv l

F = tension in the string

µ = linear density = mass/Length

F

Constructive

Interference in a String

Destructive Interference

in a String

Speed of sound waves depends on the material

through which they travel

lfv

Vibration of an object drives a longitudinal wave in

the air (or other material) molecules to create sound

The Intensity of Sound

24area

power

r

PI

0

10logI

I

• The speed of sound in a solid

– Y is the Young’s Modulus of

the material

– ρ is the density of the material

Yv

• The speed of sound in a liquid

– B is the Bulk Modulus of the liquid

– ρ is the density of the liquid

Bv

331 /273

Tv m s

K

• The speed of sound increases with temperature, in air:

– T is in Kelvin

• Start ID in 2nd column

• Write: Name, 11:30, Post-test