Chs. 13-14

Question 1

Simple Harmonic Motion: Force of Spring

Answer 1

Fs= -kx

Question 2

Simple Harmonic Motion: acceleration

Answer 2

a = -kx/m

Question 3

Elastic Potential Energy

Answer 3

PE = 1/2 kx^2

Question 4

Velocity with simple harmonic motion

Answer 4

v = +/- √k/m (A^2-x^2)

Question 5

Period of an object moving with simple harmonic motion

Answer 5

T = 2π√m/kj

Question 6

Frequency of an object-spring system

Answer 6

ƒ= 1/T
ƒ= 1/2π√k/m

Question 7

Angular Frequency

Answer 7

omega = 2πƒ = √k/m

Question 8

Position of an object in simple harmonic motion

Answer 8

x = Acos (2πƒt)

Question 9

Velocity of an object in simple harmonic motion

Answer 9

v = -A omega sin (2πƒt)

Question 10

Acceleration of an object in simple harmonic motion

Answer 10

a = -A omega^2 cos (2πƒt)

Question 11

Maximum Velocity of an object in simple harmonic motion

Answer 11

v = Aomega

Question 12

Maximum Acceleration of an object in simple harmonic motion

Answer 12

a = A omega^2

Question 13

Period of a simple pendulum

Answer 13

2π√L/g

Question 14

Transverse Wave

Answer 14

the elements of the medium move in a direction perpendicular to the direction of the wave; a wave on a stretched string

Question 15

Longitudinal Wave

Answer 15

elements of the medium move parallel to the direction of the wave velocity; a sound wave

Question 16

Velocity and Wavelength

Answer 16

v = ƒλ

Question 17

Speed of Waves on Strings

Answer 17

v = √F/(M/L)

Question 18

Superposition Principle

Answer 18

if two or more traveling waves are moving through a medium, the resultant wave is found by adding the waves together point by point

Question 19

Speed of Sound in a fluid

Answer 19

v = √B/ ρ
B = bulk modulus

Question 20

Speed of a longitudinal wave in a solid rod

Answer 20

v = √Y/ ρ

Question 21

Speed of sound in air

Answer 21

v= 331√T/273

Question 22

Intensity of a wave

Answer 22

I = P/A
P = sound power

Question 23

Relative Intensity of sound (the intensity we hear sounds)

Answer 23

β = 10 log (I / Ii)
Ii = 1.0 x 10^-12 (sound at threshold of hearing)
given in decibels

Question 24

Intensity of a Spherical Wave; intensity of a sound at a distance away

Answer 24

I = Pav/4πr^2

Question 25

Ratio of intensities at two different distances away

Answer 25

I1/I2 = r2^2/r1^2

Question 26

Doppler Effect: when the observer is moving relative to a stationary source

Answer 26

ƒo = ƒs ((v + vo)/v)

Question 27

Doppler Effect: when the source is moving relative to the observer

Answer 27

ƒo = ƒs (v/(v-vs))

Question 28

Doppler Effect: General Case

Answer 28

ƒo = ƒs ((v+vo)/(v-vs))

Question 29

Mach Number

Answer 29

Ratio between speed of object and speed of sound

Question 30

Constructive Interference Equation

Answer 30

r2 - r1 = n λ

Question 31

Destructive Interference Equation

Answer 31

r2 - r1 = (n + 1/2) λ

Question 32

Fundamental Frequency (and thus following frequencies)

Answer 32

``` ƒn = nƒ1 = n/2L √F/(M/L) n = 1, 2, 3 (harmonics) ```

Question 33

Second Harmonic Description on a String

Answer 33

Length of String = λ 2 antinodes 3 nodes

Question 34

Third Harmonic Description: String

Answer 34

L = 3/2 λ 4 nodes 3 antinodes

Question 35

Fourth Harmonic Description: String

Answer 35

L = 2 λ 5 nodes 4 antinodes

Question 36

First Harmonic Description: String

Answer 36

L = 1/2 λ 2 nodes 1 antinodes

Question 37

First Harmonic Description: open-end air column

Answer 37

L = 1/2 λ 1 node 2 antinodes

Question 38

Second Harmonic: open-end air column

Answer 38

L = λ 2 nodes 3 antinodes

Question 39

Third Harmonic: open-end air column

Answer 39

L = 3/2 λ 3 nodes 4 antinodes

Question 40

Frequency of open end air columns

Answer 40

``` ƒ = n (v/2L) = nƒ1 n = harmonic ```

Question 41

Frequency of closed end air column

Answer 41

ƒ = n (v/4L) = nƒ1

Question 42

First Harmonic: closed-end air column

Answer 42

L = 1/4 λ 1 node 1 antinode

Question 43

Third Harmonic: closed end air column

Answer 43

L = 3/4 λ 2 nodes 2 antinodes

Question 44

Fifth Harmonic: closed end air column

Answer 44

``` L = 5/4 λ 3 nodes 3 antinodes (remember, closed end air columns have no even harmonics) ```

Question 45

Frequency of a Beat

Answer 45

ƒb = ƒ2 - ƒ1