Harmonics

Question 1

define beat

Answer 1

when you play two different waves that are VERY CLOSE in wavelength/frequency but not quite the same, creating a summed wave that passes through areas of constructive and destructive interference

Question 2

what is simple harmonic motion?

Answer 2

anything with a LINEAR restoring force directly proportional to the displacement, centered around equilibrium

works with ANYTHING that has a restoring force, like homeostasis, blood pressure, or financial markets, or trying to push something back to equilibrium

if the force is roughly linear, you get this motion

Question 3

Hooke’s law

Answer 3

F = -kx, negative because restoring force = always opposite to displacement

Question 4

energy of a spring (U(s))

Answer 4

1/2 * k * x^2

x = distance from EQUILIBRIUM, thus AMPLITUDE

Question 5

where is potential energy greatest at a spring pulled in fully at -a and spread out max at a? where is it going the fastest?

Answer 5

both, push vs. pull

fastest at midpoint between -a and a, or 0

Question 6

where is force, acceleration, and velocity greatest, least, and 0 on a spring?

Answer 6

force and acceleration: greatest at ends, 0 at point 0 of equilibrium

velocity: greatest at 0, none at ends

Question 7

CALCULUS TIME, derive F = -kx into a position function

Answer 7

F = -kx
ma = -kx
a = -k/mx
second deriv (x) w/ respect to time = -k/mx(t)

the original function must be sin or cos, making it negative

Question 8

position as a function of time

Answer 8

x = Asin(omega * t)

or

x = A sin (2*pi/torque * time)

Question 9

Period vs. frequency

Answer 9

inverses, period = seconds / cycle

frequency = cycles / second

period, T = 1/f

f = 1/T

Question 10

Period of a spring vs. period of a pendulum

Answer 10

Tp = 2 * pi (sqrt(l / g))

Ts = 2 * pi * (sqrt(m/K))

Question 11

k, spring constant

Answer 11

Newtons per meter

Question 12

a 200 g mass is attached to a spring, creating a simple harmonic motion w/ a period of .25 s. if the total energy of the system = 2 J, find
(a) the force constant of the spring

(b) the amplitude of the motion

Answer 12

(a)
Ts = 2*pi * sqrt(m/k)

plug in and get 126.33

(b)

we know that at the turning point all of the energy is stored as potential energy, and thus the 2 J should be equal to the potential energy equation of the spring

2 = 1/2 * kx^2

and we know that AMPLITUDE is equal to the x as x = distance from equilibrium, so plug in k from part a and solve!

Question 13

determine height

9.4 second period,

pendulum from a tower

Question 14

how does tension impact wave speed?

Answer 14

increased tension = increased speed, thicker/denser materials = slower

speed = square root of (tension/mass/length)

AKA
sqrt tension/ linear mass-

Question 15

longitudinal wave and the wavelength of it

Answer 15

AKA compression wave, fixed point (like coil on slinky) moving PARALLEL back and forth IN THE DIRECTION OF the wave motion, instead of peaks and valleys you have compressed areas and rarefactions (low density area)

wavelength = distance between compressions OR distance between rarefactions

EX. soound

Question 16

compression vs. rarefaction

Answer 16

high molecular density/pressure vs. low molecular density/pressure

Question 17

transverse wave

Answer 17

medium vibrates PERPENDICULAR to the wave direction (up and down light wave)

Question 18

when thinking waves/discerning between types always think about how _______ is moving

Answer 18

a fixed point in the medium

Question 19

interference pattern

Answer 19

waves from different sources arrive at the same place and time

Question 20

constructive vs. destructive interference

Answer 20

constructive: two waves AT THE SAME LOCATION overlap (ex. peak + peak) and add to create a larger amplitude crest, amplitude = directly sum of waves A and B

destructive: two waves at OPPOSITE locations (ex. Peak + trough) collide to cancel each other out

Question 21

when waves collide, do they bounce off?

Answer 21

no, they pass THROUGH each other as if they never collided (even in destructive interference, they pass through after they are no longer in the same place)

Question 22

active vs. passive noice cancelling

Answer 22

active = creates opposite sounds to outside ambient noise

passive = insulation

Question 23

what type of interference is “in phase?” which is “out of phase?’

Answer 23

constructive = in phase, everything lines up

destructive = out of phase, everything lines up to CANCEL OUT

Question 24

when waves hit a wall/fixed source….

and when they have a “free end…”

Answer 24

they are inverted

they are not inverted

Question 25

standing waves

Answer 25

special frequency of wave interference (constructive AND destructive) where there are nodes of complete destructive interference (nodes) and antinodes (complete CONSTRUCTIVE interference) where amplitudes are at minimums and maximums respectively

Question 26

simplest standing wave and the frequency necessary to create it

Answer 26

half of a wavelength, just one peak

L = lambda/2
lambda = 2L

we know v = lambda * f

thus,
f = v/2L

Question 27

standing wave equation

Answer 27

for the nth harmonic, (amount of wavelengths)

f = n * v / 2L

n = number of antinodes

Question 28

beat frequency

Answer 28

at what frequency the final beat wave (summed both waves) it gets louder and quieter

Question 29

how many times with a wave with a frequency of 303 Hz match a wave with 300 Hz?

Answer 29

3 times PER SECOND, think the runner analogy, its just the difference between the two wave/second values (f1 - f2)

Question 30

Doppler effect

Answer 30

car eeeeeeeuuuuuuuuiyour sound has a higher frequency from the front than from behind because its moving, the sound waves are more compressed

a moving source emits waves that are close together in the direction it is moving (shorter wavelength, thus higher frequency)

Question 31

how does the Doppler effect work if sound has a constant speed?

Answer 31

because its the SOURCE catching up to the sound a little bit, after all sounds are emitted they move at the same speeed. this does not violated sound’s constant speed in air at all.

Question 32

when does the Doppler effect take effect?

Answer 32

when EITHER/OR the source AND the hearer are moving, if you run towards the sound its still higher freq.

Question 33

explain the sonic boom

Answer 33

if the source is moving at the speed of sound or faster, it causes an EXTREME form of the Doppler effect. as you keep moving, the peaks keep piling up on top of each other, creating a MASSIVE soundwave

Question 34

equation for Doppler effect frequency

Answer 34

f= frequency of what observer will hear
f0 = frequency of source
v = speed of wave through medium

v0 = speed of observer
vs = speed of source

f = f0( (v +/- v0) / (v -/+ vs)

• = source going toward observer
  + = source going away from observer
  vs OR v0 = 0 if the source or observer is not moving

Question 35

use the Doppler effect:
what frequency does an observer hear if an 800 Hz whistle is:
(a) moving toward the listener at 10 m/s
(b) listener moving towards whistle at 10 m/s
(c) moving away from listener at 10 m/s

Answer 35

speed of sound = 343 m/s —> 340 m/s

a. f = 800 * (340/ (340-10))
f = 824 Hz

b. 824 Hz

c. 777 Hz

Question 36

equations for frequencies in a string (held in place on both ends), air column (open/open) and another air column (open/closed)

Answer 36

string (held in place on both ends)
boundary conditions: nodes at both ends
fn = n * v/2l, n = 1, 2, 3….

air column (open/open)
boundary conditions: antinodes at both ends
fn = n * v/2L, n = 1, 2, 3….

air column (open/closed):
boundary conditons: node at closed/antinode at open
fn = n * v/4L, n = 1, 3, 5, 7….