Waves (Sound / EM) (10-12)

Question 1

MECHANICAL WAVES

Question 2

Hooke’s law

Answer 2

• F = -kx
  ○ Where k is the spring constant with units N/m
  ○ Where x is the distance between position now and original

Question 3

Wave properties
- Amplitude

- Wavelength

- Frequency 

- Period

- Speed

- Energy
	
- Intensity

Answer 3

○ Maximum distance between from the peak to the midpoint of the wave
○ Half max to min distance
○ SI unit in meters
○ A used to denote

	○ The shortest distance between any 2 identical points on a wave 
	○ SI unit in meters
	○ Lambda used to denote 

	○ The number of vibrations (cycles) per second
	○ SI unit s^-1 or Hz
	○  f used to denote
	○  f = 1/T

	○ The time to complete one cycle
	○ SI unit in seconds 
	○ T used to denote 
	○ T = 1/f

	○  a wave travels 1 wavelength in the time of 1 period
	○  v = f*lambda
	○ v is used to denote 
	○  v(sound) = 343m/s in the air 
	○  v(light) = 3*10^8 m/s

	○ The energy transported through a wave is proportional to the amplitude squared
	○ E = 1/2kA^2
		§ Where k is the spring constant
		§ Where A is amplitude

	○ Is a measure of how much energy arrives every second on 1 square meter
	○ J/s/m^2 or W/m^2
	○ I = P/4pi*r^2
	○ I1/I2 = R^2(1)/R^2(2)
		§ Where P is power
		§ Where A is area

Question 4

Speed of the wave

Answer 4

• v = f*lambda

Question 5

Energy transported by a MECHANICAL wave

Answer 5

• E = 1/2kA^2
  ○ Where k is the spring constant
  ○ Where A is amplitude

Question 6

Intensity of a wave

Answer 6

• I = P/A (DONT USE)
  
  • I = P/4pi*r^2
  • I1/I2 = R^2(1)/R^2(2)
    ○ Where P is power
    ○ Where A is area
    ○ Where R is radius

Question 7

Period of simple harmonic oscillator

Answer 7

• T = 2pi*sqrt(m/k)
  ○ Where m is mass of the mass
  ○ Where k is the spring constant

Question 8

Period of a pendulum

Resonance frequency of a pendulum

Answer 8

• T = 2pi*sqrt(L/g)
  □ Where L is the length of the pendulum
  • f = 1/2pi*sqrt(L/g)
    □ Where L is the length of the pendulum

Question 9

Diffraction

Answer 9

• Theta(in radians) = lambda/L
  □ Where lambda is wavelength
  □ Where L is the width/size of an object

Question 10

Standing waves on a string

Answer 10

• L = n*(lambda(n)/2)
  □ Where L is the distance
  □ Where n is a positive integer
  
  • f(n) = n(v/2L)
    □ Where n is a positive integer
    □ Where f(n) is the fundamental frequency

Question 11

Speed of transverse waves

Answer 11

• v = sqrt(F(t)*L/m)
  ○ Where F(t) is tension on the cord
  ○ Where L is the length of the wire

Question 12

Musical frequencies

Answer 12

• f(n) = 2^(n/12)*f(a)
  ○ Where n is the number of the note where C is 1
  ○ Where f(a) is frequency of A (440)

Question 13

Speed of longitudinal waves

Answer 13

• v = sqrt(B/roe)
  ○ Where B is the bulk modulus
  ○ Where roe is density

Question 14

Phase difference

Answer 14

• Delta lambda = vt
  
  • Delta theta = (delta lambda/lambda)*360
    Theta = vt/lambda

Question 15

SOUND WAVES

Question 16

Sound level

Answer 16

• B = 10log(10)(I/I(0))
  ○ Where I is intensity
  ○ Where I(0) is the reference intensity = 110^-12 W/m^2

Question 17

Overtone frequencies
- Open pipes

- Closed pipes

Answer 17

○ f(1) = v/2L
○ f(n) = n*f(1)
§ Where n is an integer
§ Where f(1) is the fundamental frequency

-  f(1) = v/4L
-  f(n) = n*f(1)
	§ Where n is an ODD integer
	§ Where f(1) is the fundamental frequency

Question 18

Sound intensity

Answer 18

• I = 2roev(pif*A)^2
  ○ Where roe is density
  ○ Where v is velocity
  ○ Where f is frequency
  ○ Where A is amplitude

Question 19

Constructive interference

Destructive interference

Answer 19

• Abs(d1-d2) = n*lambda
  ○ Where n is an integer
  • Abs(d1-d2) = 1/2n*lambda
    ○ Where n is an integer

Question 20

Beats
- Beat frequency

- Average frequency

Answer 20

○ f(beat) = abs(fA-fB)

	○  (f1 + f2)/2

Question 21

Doppler shift

Answer 21

• f(o)/f(s) = ((v(sound)+-v(o))/(v(sound)-+v(s)))

   ○ Where + is when OBSERVER is moving TOWARD source (numerator)
   ○ Where - is when SOURCE is moving TOWARD observer (denominator)
       § Where v(sound) is the speed of the sound
       § Where f(o) is frequency AT the OBSERVER
       § Where f(s) is frequency AT the SOURCE
       § Where v(o) is velocity of the observer (wrt earth)
       § Where v(s) is velocity of the source (wrt earth)

Question 22

Mach

Answer 22

• Mach = speed of object/speed of sound

Question 23

EM WAVES

Question 24

Speed of EM waves

Answer 24

• v = c = f*lambda

Question 25

Intensity of light

Answer 25

- I = (E0*B0)/(2*mew0) - I = 1/2*funnye(0)*c*E0^2 - I = (cB0^2)/(2*mew0) ○ Where E0 is peak value of electric field strength ○ Where B0 is the peak value of the magnetic field ○ Where mew0 is the permeability of free space

Question 26

Diffraction due to a single aperture Double slit experiment

Answer 26

- Dsinx = m*lambda ○ Where m is an integer +- ○ Where lambda is the wavelength ○ Where D is the width of the aperture - For first dark fringe ○ Dsinx = lambda/2 - For second dark fringe ○ Dsinx = 3*lambda/2 - In general ○ Dsinx = nlambda/2 § Where n is an odd integer M*lambda/d = x/L

Question 27

QUANTUM MECHANICS

Question 28

Charge to mass ratio

Answer 28

- e/m = E/B^2*r

Question 29

Cathode rays

Answer 29

- r = mv/qB

Question 30

The quantum hypothesis

Answer 30

- E = nhv ○ Where n is a positive integer ○ Where h is plancks constant ○ Where v is the frequency of the oscillation

Question 31

Photo electric effect

Answer 31

- Ke = hv - small sigma ○ Where hi is plancks constant ○ Where v is the frequency of the oscillation ○ Where small sigma is the work function

Question 32

Photon energy Energy levels

Answer 32

- E = hc/lambda - Hf = Eu - El ○ Where Eu and El is energy upper and lower repectively ○ Where h is plancks constant ○ Where f = v which is the frequency of the oscillation - En = (2pi^2*e^4*m*k^2)/(n^2*h^2) ○ Where E(n) is the energy of the nth electron level ○ Where n is an integer ○ Where h is plancks constant ○ Where m is mass ○ Where k is coulumbs constant ○ Where e is the charge of an electron § r(1) = 5.29*10^-11

Question 33

Bohrs quantum condition

Answer 33

Bohrs quantum condition - mvr(n) = n*(h/2pi) ○ Where m is mass ○ Where v is velocity ○ Where n is integer ○ Where r(n) is the radius of the nth electron orbit ○ Where h is plancks constant - r(n) = (n^2*h^2)/(4pi^2*m*k*e^2) ○ Where r(n) is the radius of the nth electron orbit ○ Where n is an integer ○ Where h is plancks constant ○ Where m is mass ○ Where k is coulumbs constant ○ Where e is the charge of an electron § r(1) = 5.29*10^-11

Question 34

Momentum of a photon

Answer 34

- p = h/lambda - Lambda = h/p ○ Where p is momentum ○ Where h is plancks constant ○ Where lambda is wavelength

Question 35

- Binding energy

Answer 35

○ Binding energy = Mass(constituent parts) - mass(nucleus) * c^2 ○ Use atomic mass units - Binding energy per nucleon = binding energy/A ○ Where A is the mass number

Question 36

- Size of nuclei

Answer 36

○ r = 1.2*10^-15*A^(1/3) ○ Where A is mass number (NOT AREA)

Question 37

Alpha decay - Transmutation equation Energy release

Answer 37

- Transmutation equation ○ A Z (X) -> A-4 Z-2 (X') + 4 2 (He) Energy release - m(p)c^2 = m(d)c^2 + m(a)c^2 + Q ○ Where m(p), m(d), and m(a) is the mass of the parent, daughter and alpha particles repsectively ○ Where c is the speed of light ○ Where Q is the disintegration energy (kinetic energy)

Question 38

Kinetic energy of an alpha particle - Kinetic energy - Charge

Answer 38

Kinetic energy of an alpha particle - m(a)*v(a) + m(d)*v(d) = 0 - m(a)*v(a) - m(d)*v(d) = 0 ○ Where m(a) and m(d) is the mass of the alpha and daughter particle respectively ○ Where v(a) and v(d) is the velocity of the alpha and daughter particle respectively - Kinetic energy ○ Ke(a) = 1/2m(a)*v(a)^2 § Where m(a) is the mass of the alpha particle § Where v(a) is the velocity of the alpha particle - Charge ○ Q = Ke(a) + Ke(d)

Question 38

Beta decay

Answer 38

- n -> p + e- + vbar ○ Where n is the original element ○ Where p is the element with an extra proton ○ Where e- is an electron ○ Where vbar is a neutrino

Question 39

Gamma decay - A Z (N*) -> A Z (N) + gamma ○ Where N* is the atom in its excited state ○ Where gamma is a high energy photon

Answer 39

- A Z (N*) -> A Z (N) + gamma ○ Where N* is the atom in its excited state ○ Where gamma is a high energy photon

Question 40

Nuclear fission Energy released in nuclear fission

Answer 40

- n + 1 1 (H) -> 2 1 (H) + gamma - E = (m(i) - m(f))*e ○ Where m(i) is the initial mass ○ Where m(f) is the final mass ○ Where e is the electron energy (935.1MeV)