Physics Class 5 - DC Circuits, Oscillators, Waves, and Sound

What are Kirchhoff’s rules?

1. Currents into and out of any point in a circuit must equal one another

   1. Continuity

   2. Conservation of charge

   3. Elements in series have equal current

2. Sum of voltages around any closed loop in a circuit must be equal to zero

   1. Conservation of energy

   2. Elements in parallel have same voltage

What is the equation for power?

P = IV = IR² = V²/R

P = power

I = current

V = voltage

R = resistor

How is energy dissipated by resistors?

Thermal energy

What is the form of power output by a battery?

Electrical energy

What is the rule for currents through elements of a series?

Elements in a series experience the same current running through them

What is the total resistance for elements in parallel?

(R_aR_b)/(R_a + R_b)

What are elements in series? Parallel?

Series: in a line, same current

Parallel: in parallel sides of a loop, same voltage

What is a voltmeter?

Measures voltage

Connect in parallel to circuit segment of interest

High internal resistance

What does high internal resistance do in voltmeters?

Minimizes impact of measurement on the circuit

What is an ammeter?

Measures current

Connect in series to the circuit segment of interest

Low internal resistance

Why do you want low internal resistance on an ammeter?

It is in series, so you want it not to affect how the current flows through it

What is the equation for force exerted by a magnetic field?

T = teslas

q = absolute value of the charge

v = speed

B = magnitude of magnetic field

What is the magnetic field if theta is 0 or 180 degrees?

0

How do you use the right hand rule for magnetic fields?

Thumb points in direction of v

Fingers in the direction of B (fingers = field)

Palm gives direction of F_B for a positive charge

Back of hand gives direction of F_B for negative charge

What is F_B perpendicular to?

v (speed) and B (magnetic field)

What does a circle with a dot mean in terms of magnetic field?

It is pointing out of the screen, towards me

What is work done by a magnetic field?

A charge entering a magnetic field will move in a circular path = centripetal force

Work done will be 0, as it is always when considering centripetal force

What are magnetic fields?

Created by moving charges

What is a current?

Motion of positive charges

How do you find the direction of a magnetic field using currents?

Point thumb of right hand in direction of current

Fingers curl in direction of magnetic field

The magnetic field at a point in space is tangent to the magnetic field there

What does a circle with a cross through it mean in magnetic field vectors?

The vector is pointing away from you, into the field

How are large magnetic fields created?

By permanent magnets made of materials like iron, cobalt, and nickel that create large magnetic fields due to alignments of their electron spin

Produces magnetic field without having a current applied to it

How do magnetic field lines relate to the North and South poles of a permanent magnet?

Magnetic field lines enter the south pole and exit the north pole

What is simple harmonic movement?

Back and forth motion

Force is proportional to the negative of the displacement

What is Hooke’s law?

F = -kx

F = restoring force

k = spring constant

x = displacement from equilibrium

What is amplitude?

Greatest displacement from equilibrium during oscillation

What is a period?

Time to complete one cycle

Constant for simple harmonic motion

Independent of amplitude for simple harmonic motion

What is frequency?

Number of cycles per second

f = 1/T

f = frequency

T = period

For springs: f = (1/2pi) sqrt (k/m)

k = spring constant

m = mass

What is the energy stored in a compressed spring?

PE_elastic = ½ kx²

What is the Work done by a spring?

W = - (change in PE)

How do you figure out the energy in a spring system?

KEi + PEi = KEf + PEf

In absence of non-conservative forces

How does V_max of a spring system relate to amplitude?

V_max = sqrt (k/m) A

Directly proportional

What is the frequency of a pendulum?

f = 1/2pi (sqrt (g/L))

L = length

Angle in radians measured from vertical

String is massless and frictionless

What is the restoring force of a pendulum?

mg sin theta = F_restore

In radians

sin theta ~ theta when the angle is small, therefore force is proportional to force

What is a wave?

Propagating oscillations that transfer energy

What is wavelength, amplitude, wave speed, and period for a wave?

Wavelength (lambda) = length of one cycle

Amplitude (A) = max displacement from equilibrium

Wave speed (v) = speed of wave energy propagation

Period (T) = time required for one oscillation

What are trasverse waves?

Oscillations perpendicular to direction of wave propagation

Ex: ocean waves, wave on a string, electromagnetic waves

What are longitudinal waves?

Oscillation parallel to wave propagation

Ex: sound (longitudinal pressure waves)

What is a compression, rarefaction?

Compression: in longitudinal wave, when a bunch of particles are oscillating so they are close together

Rarefaction: in longitudinal waves, when a bunch of particles are oscillating far apart

Wavelength is distance between compressions or rarefactions

What is wave speed?

v = (wavelength) (frequency)

What are the two big rules for waves?

1. Speed of a wave in a medium depends on the type of wave and physical properties of medium

   1. v is constant in the same medium, regardless of frequency of wavelength

2. A wave moving form one medium to another will maintain the same frequency

   1. f is constant between media

If a wave crosses a boundary, what must be true?

Some is reflected backwards, while some continues travelling through

Some energy is not transmitted, some is reflected back

What is constructive interference?

Waves are in phase

When two + waves combine, their displacements add

Final amplitude is greater than that of either wave

d + d = A

What is destructive interference?

When two or more waves combine, displacements add

Waves are out of phase (by half a cycle)

Final amplitude is smaller than that of both waves

d - d = A

What is beat frequency?

Two waves with different frequencies combine

Cycles between constructive and destructive interference are beats

f_B = |f₁ - f₂|

What is a standing wave?

Waves are trapped

Wave interferes with its own reflection → does not propagate (move left/right)

What is a node? Antinode? In terms of pressure and displacement

Pressure node: where pressure is zero

Displacement node: displacement is zero (point of zero oscillation)

Pressure antinode: pressure is max

Displacement antinode: displacement is max (max oscillation)

Pressure node = displacement antinode and vice versa

In a pipe with one end open, what nodes are always true?

Closed end is always a displacement node, pressure antinode

Open end is always a pressure node, displacement antinode

If a string is tied at both ends, what is the frequency, wavelength?

f_n = nf₁

Wavelength _n = 2L/n

What is the first harmonic?

Longest wavelength standing wave that can exist on a string tied on both ends

n = 1

½ wave

1 displacement node, 2 displacement antinodes

What is a second harmonic? Third?

Second: n = 2; two displacement nodes and three antinodes; 1 wave

Third: n = 3; three displacement nodes, four antinodes; 1.5 waves

What is intensity?

Energy of a wave incident per unit area per unit time

I = power/area

Units = [I] = Watts/m²

What is the intensity of a spherical wave?

I = P/(4pi*r²)

I is proportional to 1/r²

I is proportional to amplitude²

Spherical waves are those going in all directions (ex: sound from a speaker)

What is sound intensity equation? What is the threshold of human hearing?

B = 10 log₁₀ I/I_o

I_o = 10^-12 W/m²

Units: [B] = dB (decibels)

How do you work logarithms related to human hearing?

For every increase in the I by a factor of 10, add 10 to B (ex: if increases by factor of 100, add 20 b/c 10 + 10)

For every decrease of I by factor of 10, subtract 10 from B

What is the doppler effect?

Shift in detected frequency of a wave due to relative motion between detector and sound source

Detector and sound source move closer → higher detected frequency and vice versa

This does not mean frequency is increasing/decreasing → velocities are constant, so detected frequency is constant

How is doppler shift calculated?

f_D = f_s (v ± v_D)/(v -/+ v_S)

Use top sign when motion is toward

f_D = frequency detected

v_D = speed of detector

v_S = speed of sound source

v = speed of sound wave (350 in air)

What is the speed of sound in air?

350 m/s ish