JEE/NEET Physics · Oscillations & Waves series · Part 5 of 8 · All parts →
- A wave = oscillation that travels, carrying energy (not matter)
- Transverse: jiggle ⊥ travel (strings, light) · Longitudinal: jiggle along travel (sound)
- The master link: v = f × λ (speed = frequency × wavelength)
- String wave speed: v = √(T/μ) — tighter or lighter = faster
- Sound in air ≈ 343 m/s; light ≈ 3×10⁸ m/s — a million-fold apart
Drop a stone in a pond: the ripples travel outward, but the water itself just bobs in place. The jiggle travels; the stuff stays home. That’s a wave — and it’s how light, sound, earthquakes, WiFi and every word you’ve ever heard actually reach you. Part 5 of the Oscillations & Waves series.
- What actually travels
- Transverse vs longitudinal
- The master link: v = fλ
- What each letter means
- String speed and sound speed
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
What Actually Travels
Watch a floating leaf as ripples pass: it bobs up and down — it does NOT travel with the wave. The wave carries energy and pattern, not material. This single picture answers half of wave physics: the medium oscillates in place; the disturbance moves on.
Transverse vs Longitudinal
| Type | Jiggle direction relative to travel | Examples |
|---|---|---|
| Transverse | perpendicular (⊥) — like shaking a rope side-to-side | string instruments, water ripples, light and all EM waves |
| Longitudinal | along (∥) — push-pull compressions like a slinky | sound in air, P-earthquake waves |
Sound is push-pull: air squeezes and stretches along the travel direction — your eardrum is pushed and pulled, not lifted.
The Master Link: v = fλ
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| v | wave speed — set by the MEDIUM, not the source | m/s: air-sound 343; string varies; light 3×10⁸ |
| f | frequency — set by the SOURCE (how fast it’s shaken) | Hz |
| λ (lambda) | wavelength — distance between successive crests | m |
The crucial logic: when a wave crosses into a new medium, v changes — so λ changes to compensate, but f stays fixed (the source set it). This one line — ‘frequency constant, wavelength adjusts’ — resolves most medium-change questions instantly.
String Speed and Sound Speed
Guitar tuning is this formula: tighten the string (↑T) → faster waves → the fixed string length now fits more wavelengths → higher pitch. And sound speeds up in hotter air (faster molecules) — ~0.6 m/s per °C.
Solved Examples
λ = v/f = 340/500 = 0.68 m.
Check: audible sound waves are human-scale — about half a metre to a few metres. ✔
Answer: λ = 0.68 m
Frequency is locked by the source: 500 Hz stays — pitch unchanged.
Wavelength adjusts: λ = 1480/500 ≈ 2.96 m — 4.35× longer, exactly the speed ratio.
✔ (This is why ‘frequency constant’ is the master key.)
Answer: λ ≈ 2.96 m; pitch unchanged
v ∝ √T: ×√1.21 = ×1.1 → speed +10%.
Pitch: for a fixed string, f = v/2L → f also ×1.1 — about a musical half-step up. Tuning pegs are √T in hardware. ✔
Answer: speed ×1.1 (pitch +10%)
- Believing the medium travels. Only energy and pattern move; the material bobs in place (the leaf).
- Changing f at a medium boundary. Frequency is the source’s property — constant across media; λ does the adjusting.
- Using v = fλ with mixed units. MHz needs ×10⁶; cm needs ÷100. One slip, thousand-fold errors.
- Sound in ‘light units’. Sound needs matter (it’s molecules pushing); light needs none — that’s why space is silent but sunlit.
This Physics in Your Daily Life
- Tuning any string instrument is √(T/μ) by hand — every peg turn is this card.
- Thunder counting: light arrives instantly; sound takes ~3 s per kilometre. Count seconds ÷ 3 = km to the lightning — v = fλ’s speed, as a folk trick.
- WiFi and radio bands: 2.4 GHz waves ≈ 12.5 cm; 5 GHz ≈ 6 cm — the shorter wavelength penetrates walls worse: your router’s dead spots are wavelengths.
- Whales and elephants call across kilometres with very low frequencies (huge λ) that travel for miles — big wavelength, long reach.
- Ultrasonography uses MHz wavelengths (millimetre-scale) — small λ resolves small details: the resolution logic of every scan.
Practice set (answers hidden — try first)
(NEET-level) v = 340 m/s, f = 170 Hz. λ:
(Concept) Sound enters water. What stays constant?
(JEE Main-level) String tension ×4. Wave speed:
(NEET-level) Sound is what type of wave in air?
(JEE Main-level) A 100 MHz FM wave (v = 3×10⁸): λ =
- 🧠 Chant: ‘the source sets the beat, the medium sets the speed’.
- 🧠 Boundary rule: ‘frequency holds, wavelength bends’.
- 🏠 Daily: count thunder seconds ÷ 3 = kilometres — wave speed as weather folklore.
- 🏠 Daily: your router’s 5 GHz dead spots are short wavelengths failing at walls.
- 🔁 wave = travelling oscillation; medium bobs in place
- 🔁 transverse vs longitudinal by jiggle direction
- 🔁 v = fλ; f fixed by source; v fixed by medium
- waves carry energy and pattern — the medium stays put
- transverse ⊥ (strings, light); longitudinal ∥ (sound)
- v = fλ — speed by medium, frequency by source
- medium change: f constant, λ adjusts
- string: v = √(T/μ) — tuning pegs are √T
Quick revision
- A wave = oscillation that travels, carrying energy (not matter)
- Transverse: jiggle ⊥ travel (strings, light) · Longitudinal: jiggle along travel (sound)
- The master link: v = f × λ (speed = frequency × wavelength)
- String wave speed: v = √(T/μ) — tighter or lighter = faster
- Sound in air ≈ 343 m/s; light ≈ 3×10⁸ m/s — a million-fold apart
- Transverse vs longitudinal
Have a doubt on this topic?
