8.2 Waves, Sound, Light, Heat, Electricity, and Magnetism

8.2 Waves, Sound, Light, Heat, Electricity, and Magnetism

This section covers everything in AdUCET-level physics that is not mechanics: how energy travels as a wave, how we hear and see, how heat moves, and how charge and magnetism drive the circuits in a house. Force, motion and energy conservation are treated in section 8.1 and are not repeated here.

Wave Anatomy and the Wave Equation

A wave transports energy without permanently transporting matter. Four measurements describe any wave:

• Wavelength ($\lambda$) — the distance between two consecutive crests, in metres.
• Frequency ($f$) — cycles passing a point each second, in hertz (Hz).
• Period ($T$) — the seconds per cycle. Frequency and period are reciprocals: $T = 1/f$.
• Amplitude — the maximum displacement from the rest position, which sets how much energy the wave carries.

These combine in the wave equation:

$v = f\lambda$

Worked example 1. Sound travelling at 340 m/s has a wavelength of 0.85 m.

1. Rearrange: $f = v/\lambda = 340 \div 0.85 = 400$ Hz.
2. Period: $T = 1/f = 1 \div 400 = 0.0025$ s, that is 2.5 milliseconds.
3. Sanity check: $400 \times 0.85 = 340$ m/s. Correct.

Because $v$ is fixed by the medium, frequency and wavelength are inversely proportional: raising the pitch shortens the wavelength.

Four wave behaviours

1. Reflection — the wave bounces off a boundary; the angle of incidence equals the angle of reflection.
2. Refraction — the wave bends because its speed changes when it enters a new medium. A spoon looks broken in a glass of water for this reason.
3. Diffraction — the wave spreads out after passing an edge or a narrow gap, which is why you hear a conversation around a corner.
4. Interference — two waves overlap. Crest on crest gives constructive interference and a larger amplitude; crest on trough gives destructive interference and cancellation.

The Doppler effect is the apparent change in frequency when the source and observer move relative to each other. An approaching ambulance siren sounds higher because the waves in front are bunched up; as it passes, the pitch drops. The same effect redshifts light from receding galaxies.

Sound

Sound is a longitudinal mechanical wave, so it cannot travel through a vacuum — a bell ringing inside a jar goes silent as the air is pumped out. Pitch is set by frequency (a healthy young ear hears roughly 20 Hz to 20,000 Hz), and loudness is set by amplitude and is reported in decibels (dB).

Sound moves fastest in solids and slowest in gases, the opposite of light, because tightly packed particles pass on the compression quickly: about 343 m/s in air at 20 degrees Celsius, about 1,480 m/s in water, and about 5,000 m/s in steel. Heating air also speeds sound up.

Resonance happens when a driving frequency matches an object's natural frequency, so the amplitude builds — the physics behind a guitar's soundbox and the shattering of a wine glass. An echo is simply reflected sound; the reflecting surface must be roughly 17 m away before the human ear separates the echo from the original.

Light and the Electromagnetic Spectrum

Electromagnetic waves are transverse, need no medium, and all travel at $c = 3.0 \times 10^8$ m/s in a vacuum. In order of increasing frequency and energy, and therefore decreasing wavelength:

Within the visible band the order ROYGBIV runs from red, with the longest wavelength and lowest energy, to violet, with the shortest wavelength and highest energy. A prism separates white light because each colour refracts by a slightly different amount. An object looks green because it reflects green and absorbs the rest; a black object absorbs nearly everything. The sky is blue because air molecules scatter short blue wavelengths far more strongly than long red ones, and a Manila Bay sunset is red because the low sun's light travels through so much atmosphere that the blue is scattered away before it reaches you.

Mirrors, lenses, and total internal reflection

A real image forms where light rays physically meet and can be caught on a screen; a virtual image only appears to come from behind the mirror or lens and can never be projected. Total internal reflection occurs when light travelling from a denser to a less dense medium strikes the boundary beyond the critical angle and reflects entirely back inside — the working principle of fibre-optic cables and the sparkle of a cut diamond.

Heat and Thermodynamics

Temperature measures the average kinetic energy of particles; heat is the thermal energy that flows from a hotter body to a cooler one. A tub of lukewarm water contains far more heat than a red-hot nail even though the nail's temperature is much higher.

Worked example 2. Convert 40 degrees Celsius, then convert 77 degrees Fahrenheit back.

1. $F = \tfrac{9}{5}(40) + 32 = 72 + 32 = 104^\circ$F, and $K = 40 + 273.15 = 313.15$ K.
2. $C = \tfrac{5}{9}(77 - 32) = \tfrac{5}{9}(45) = 25^\circ$C.

Heat moves in exactly three ways: conduction through direct particle contact in solids (a metal sandok handle heating up), convection through the bulk movement of a fluid (boiling sinigang, and the sea breeze that cools a coastal barangay each afternoon), and radiation as infrared waves needing no medium at all (the Sun's warmth, the heat felt from a bonfire).

Specific heat capacity ($c$) is the energy needed to raise 1 kg of a substance by 1 degree Celsius, and $Q = mc\Delta T$. Water's value is unusually high at about 4,200 J/(kg$\cdot^\circ$C), which is why coastal air stays milder than inland air.

Worked example 3. Heat 0.5 kg of water from 30 degrees Celsius to 100 degrees Celsius.

1. $\Delta T = 100 - 30 = 70^\circ$C.
2. $Q = 0.5 \times 4{,}200 \times 70 = 2{,}100 \times 70 = 147{,}000$ J, or 147 kJ.

Most materials also undergo thermal expansion, growing when heated, which is why bridges carry expansion joints and railway tracks are laid with gaps. The laws of thermodynamics in plain terms: the zeroth says two bodies each in thermal equilibrium with a third are in equilibrium with each other; the first says energy is conserved, so heat added either raises internal energy or is spent doing work; the second says heat flows spontaneously only from hot to cold and no engine can be perfectly efficient; the third says absolute zero can be approached but never reached.

Static Electricity, Current, and Circuits

Like charges repel and unlike charges attract. An object can be charged three ways: by friction (rubbing a plastic comb on dry hair so it lifts torn paper), by conduction (touching a charged body to a neutral one so they share charge and end with the same sign), and by induction (bringing a charged object near a neutral conductor so the charges separate, then grounding it, leaving an opposite charge).

• Current ($I$) is the rate of charge flow, in amperes, where 1 A is 1 coulomb per second.
• Voltage ($V$) is the potential difference that pushes charge, in volts.
• Resistance ($R$) opposes the flow, in ohms ($\Omega$).

Ohm's law ties them together: $V = IR$, so $I = V/R$ and $R = V/I$.

Worked example 4. A 6 $\Omega$ and a 3 $\Omega$ resistor are wired in parallel across a 12 V battery.

1. $\dfrac{1}{R_{eq}} = \dfrac{1}{6} + \dfrac{1}{3} = \dfrac{1}{6} + \dfrac{2}{6} = \dfrac{3}{6} = \dfrac{1}{2}$, so $R_{eq} = 2\ \Omega$ — smaller than either resistor, which is always true in parallel.
2. Total current: $I = 12 \div 2 = 6$ A.
3. Branch check: $12 \div 6 = 2$ A and $12 \div 3 = 4$ A, and $2 + 4 = 6$ A. Consistent.

Wire the same pair in series and $R_{eq} = 6 + 3 = 9\ \Omega$, giving a much smaller current of about 1.33 A. Household outlets are wired in parallel so every appliance receives the full 220 V and one failure does not kill the rest.

Electrical power is $P = VI = I^2R = V^2/R$, in watts, and utilities bill for energy in kilowatt-hours. An electric fan rated 500 W run 8 hours a day for 30 days uses $0.5 \times 8 \times 30 = 120$ kWh; at 12 pesos per kWh that is 1,440 pesos a month.

Magnetism and Electromagnetic Induction

Magnetic field lines leave the north pole and enter the south pole outside a magnet, and like poles repel. Cutting a bar magnet in half yields two complete magnets — isolated poles do not exist. Earth behaves like a giant bar magnet, and because a compass needle's north end points to geographic north, the magnetic pole sitting near geographic north is really a magnetic south pole.

An electromagnet is a coil (solenoid) carrying current, usually around a soft-iron core; its strength rises with more current, more turns, and a better core, and it can be switched off — the basis of doorbells, scrapyard cranes and relays.

Electromagnetic induction is the reverse effect: a changing magnetic field through a coil induces a voltage. Move a magnet into a coil and current flows; hold it still and nothing happens. The distinction examiners love is the direction of conversion:

• A generator turns mechanical energy into electrical energy (a hydroelectric turbine or a bicycle dynamo).
• A motor turns electrical energy into mechanical energy (an electric fan, a blender).

Common Traps

1. Assuming sound travels fastest in air. It is fastest in solids; only light slows down in denser media.
2. Confusing pitch with loudness — pitch tracks frequency, loudness tracks amplitude.
3. Reversing the electromagnetic spectrum. Gamma rays have the shortest wavelength and highest energy; radio waves are the opposite.
4. Saying a convex mirror can form a real image. It cannot; its image is always virtual, upright and smaller.
5. Treating heat and temperature as synonyms.
6. Forgetting that parallel equivalent resistance is always less than the smallest individual resistor.