14.3 Waves, Sound, and Light

Waves appear across USTET Science: earthquakes, musical notes, and rainbow colors all share the same vocabulary. This section builds a single framework—amplitude, wavelength, frequency, period, and $v = f\lambda$—then applies it to sound and light.

What Is a Wave?

A wave is a disturbance that transfers energy through oscillations. Particles of the medium (for mechanical waves) vibrate about equilibrium positions; they do not travel permanently with the wave from source to receiver. After a water wave passes, a floating leaf mostly bobs up and down near its original place.

Transverse vs Longitudinal

• Transverse wave: Oscillations are perpendicular to the direction of energy travel. Examples: waves on a string; electromagnetic waves (electric and magnetic fields oscillate perpendicular to the travel direction).
• Longitudinal wave: Oscillations are parallel to the travel direction—compressions and rarefactions. Example: sound in air.

Some waves in nature (water waves) have mixed character, but exam items usually ask you to classify clear textbook cases.

Wave Properties

Relationships you must know:

$T = \frac{1}{f}, \quad f = \frac{1}{T}$ $v = f\lambda$

Amplitude relates to energy carried: larger amplitude generally means more energy (brighter light, louder sound), while frequency relates to pitch (sound) or color (visible light).

Worked example — Wave equation

A wave has frequency 50 Hz and wavelength 2.0 m. Find its speed and period.

$v = f\lambda = (50\ \mathrm{Hz})(2.0\ \mathrm{m}) = 100\ \mathrm{m/s}$ $T = 1/f = 0.020\ \mathrm{s}$

If instead $v = 340\ \mathrm{m/s}$ (approx. speed of sound in air) and $f = 170\ \mathrm{Hz}$, then

$\lambda = \frac{v}{f} = \frac{340}{170} = 2.0\ \mathrm{m}$

Mechanical vs Electromagnetic Waves

Mechanical waves require a material medium (solid, liquid, or gas). Sound cannot travel in outer-space vacuum; astronauts need radios (electromagnetic signals) to communicate.

Electromagnetic (EM) waves—radio, microwave, infrared, visible light, ultraviolet, X-rays, gamma rays—do not need a medium. In vacuum they travel at

$c \approx 3.0 \times 10^8\ \mathrm{m/s}$

the speed of light. In glass or water they slow down; frequency stays set by the source while wavelength adjusts so $v = f\lambda$ still holds in that medium.

Sound Waves

Sound is produced by vibrating objects that create pressure variations in a medium. In air, molecules bunch into compressions and spread into rarefactions that travel outward.

• Pitch: Higher frequency → higher pitch (treble). Lower frequency → lower pitch (bass). Human hearing is roughly 20 Hz to 20,000 Hz.
• Loudness: Related to amplitude (and intensity). Larger amplitude → louder sound.
• Timbre: Quality that lets you distinguish a piano from a flute at the same pitch—linked to waveform shape and overtones (qualitative awareness is enough).

Sound travels faster in solids than in liquids, and faster in liquids than in gases, because particles in denser-bonded media can transmit disturbances more effectively (with important exceptions tied to elasticity). Thunder is heard after lightning is seen because light reaches you almost instantly compared with sound.

Echo timing (useful pattern)

If sound speed is $v$ and an echo returns after time $t$ from a wall, the one-way distance is $\frac{1}{2}vt$ because the sound travels to the wall and back.

Light and the Electromagnetic Spectrum

Visible light is a narrow band of the EM spectrum. In order of increasing frequency (decreasing wavelength): red → orange → yellow → green → blue → violet. Beyond violet lies ultraviolet; below red lies infrared. White light contains many wavelengths; a prism separates them by refraction.

Reflection

The law of reflection: angle of incidence equals angle of reflection, both measured from the normal (perpendicular) to the surface. Smooth mirrors produce clear specular reflection; rough walls scatter light diffusely so you can see the wall from many angles.

Refraction

Refraction is the bending of light as it crosses into a medium where its speed changes. Entering a slower medium (air → glass) typically bends the ray toward the normal; entering a faster medium bends it away from the normal. This is why a straight stick looks bent at a water surface and why lenses can focus images.

Qualitative Snell's-law awareness is usually enough for USTET: denser optical medium → slower light → shorter wavelength in the medium; frequency remains the same as in the incident wave.

Dispersion and Color

Different wavelengths refract by slightly different amounts in glass, spreading white light into a spectrum—dispersion. Rainbows arise from refraction and reflection in water droplets. Opaque objects look colored because they reflect some wavelengths and absorb others; a red shirt reflects red light strongly.

Interference and Diffraction (Recognition Level)

When two waves overlap, interference can be constructive (amplitudes add) or destructive (amplitudes cancel). Diffraction is spreading of waves around obstacles or through openings; it is more noticeable when the opening size is comparable to the wavelength. These ideas explain noise patterns and the fuzzy edges of shadows for some waves; you mainly need recognition vocabulary.

Connecting Back to Energy

Waves transport energy. Doubling amplitude of a mechanical wave typically increases energy by a factor related to $A^2$ (know the direction of the relationship even if the exact factor is not always tested). Light intensity falls as you move farther from a point source roughly with the inverse-square law in free space—another energy-delivery idea that can appear qualitatively.

Exam Habits for Wave Items

1. Always check whether $v$, $f$, or $\lambda$ is missing and apply $v = f\lambda$.
2. Remember $T = 1/f$ for period–frequency swaps.
3. Classify: needs medium? transverse or longitudinal?
4. For sound: pitch ↔ $f$, loudness ↔ amplitude.
5. For light: color ↔ frequency/wavelength; mirrors → reflection; lenses/water surface → refraction.
6. Compare speeds: light ≫ sound, which is why you see fireworks before you hear them.

If you can move fluently among the property table, the wave equation, and the sound-versus-light comparison chart, you are ready for the waves portion of USTET Science Physics.