Sound is a mechanical wave — it needs a medium to travel. This chapter covers wave properties, the characteristics of sound, the Doppler effect, and resonance. CDS questions focus on wave terminology (wavelength, frequency, amplitude), the speed of sound in different media, echo conditions, and the Doppler effect.
📌 CDS focuses on: Transverse vs longitudinal waves; wave parameters (λ, f, v = fλ); speed of sound in different media (fastest in solids); echo conditions; characteristics of sound (pitch, loudness, quality); Doppler effect; ultrasound applications; resonance.
1. Wave Types & Parameters
1.1
Transverse vs Longitudinal Waves
All waves transfer energy — but the particle motion differs fundamentally
Fig. 1 — Transverse waves: particles move perpendicular to propagation (light, string waves). Longitudinal waves: particles move parallel to propagation direction (sound). Sound travels as compressions and rarefactions.
⚡ Wave Parameters & Key Relation
Wave speed: v = f × λ
v = speed (m/s); f = frequency (Hz); λ = wavelength (m)
Frequency: f = 1/T (T = time period in seconds)
Amplitude (A): maximum displacement from mean position
Speed of sound at 0°C in air ≈ 332 m/s
Speed of sound increases with temperature: v ≈ 332 + 0.6T (T in °C)
Speed of sound at room temp (25°C) ≈ 346 m/s
Comparison of speeds in different media:
Solids > Liquids > Gases (sound travels fastest in solids)
In steel: ~5100 m/s; in water: ~1500 m/s; in air: ~340 m/s
Speed of light (vacuum): c = 3 × 10⁸ m/s (much faster than sound)
Sound CANNOT travel through vacuum — it needs a material medium. Light travels through vacuum. This is why we see lightning before hearing thunder — light reaches us almost instantly, sound takes several seconds.
2. Sound Characteristics & Echo
2.1
Pitch, Loudness, Quality & Echo Conditions
🎵 Pitch
Determines shrillness of sound
Depends on frequency
High frequency → high pitch (shrill)
Low frequency → low pitch (bass)
Human hearing: 20 Hz to 20,000 Hz
Infrasound: <20 Hz; Ultrasound: >20,000 Hz
🔊 Loudness
Depends on amplitude (energy of wave)
Greater amplitude → louder sound
Unit: decibel (dB)
Threshold of hearing: 0 dB
Normal conversation: ~60 dB
Pain threshold: ~120 dB
🎼 Quality (Timbre)
Distinguishes two sounds of same pitch and loudness
Depends on the waveform (presence of overtones/harmonics)
Same note on violin vs flute sounds different because of timbre
Depends on the instrument/source
⚡ Echo & Reverberation
Echo condition:
The reflected sound must reach our ears at least 0.1 second after the original.
(Human ear can distinguish two sounds separated by ≥ 0.1 s)
Minimum distance for echo: d = v × t/2 = 340 × 0.1/2 = 17 metres
So the reflecting surface must be at least 17 m away for an echo to be heard.
Reverberation: persistence of sound due to multiple reflections — shorter than echo.
Unwanted reverberation is reduced in studios by using soft furnishings.
SONAR (Sound Navigation and Ranging):
Uses ultrasound to detect underwater objects (submarines, fish).
Distance = v × t/2 (v = speed of sound in water ≈ 1500 m/s; t = time for echo)
3. Doppler Effect
3.1
Apparent Change in Frequency Due to Relative Motion
Doppler Effect: When a source of sound and an observer move relative to each other, the observed frequency is different from the actual frequency. Source approaching observer: Apparent frequency increases (sound appears higher-pitched). Source moving away from observer: Apparent frequency decreases (sound appears lower-pitched). Real-life examples: Train whistle pitch drops as it passes; ambulance siren changes pitch; police radar guns; red-shift of stars (light Doppler effect shows universe is expanding).
💡 Doppler Effect Mnemonic: Think of a train approaching — the sound waves are "bunched up" in front (shorter wavelength = higher pitch) and "stretched out" behind (longer wavelength = lower pitch). Same principle applies to light — stars moving away from us show red-shift (longer wavelength/lower frequency).
📝 CDS PYQ
Waves & Sound
Q1. The minimum distance of a reflecting surface from the source for an echo to be heard is approximately:
(a) 10 m
(b) 17 m
(c) 25 m
(d) 34 m
Answer: (b) 17 m
For an echo to be heard distinctly, the reflected sound must return at least 0.1 second after the original. Distance = v × t/2 = 340 × 0.1/2 = 17 m. This is one of the most directly tested echo facts in CDS. The "divide by 2" accounts for the sound travelling to the wall AND back.
Q2. In which medium does sound travel the fastest?
(a) Air
(b) Water
(c) Steel
(d) Vacuum
Answer: (c) Steel (solid)
Sound travels fastest in solids, slower in liquids, and slowest in gases: Solid > Liquid > Gas. Speed in steel ≈ 5100 m/s; in water ≈ 1500 m/s; in air ≈ 340 m/s. Sound cannot travel through vacuum at all (unlike light). This ordering is because solids are most rigid — molecules are tightly packed and transmit vibrations more efficiently.
Q3. The pitch of a sound depends on its:
(a) Amplitude
(b) Frequency
(c) Speed
(d) Wavelength only
Answer: (b) Frequency
Pitch is the sensation of shrillness or graveness of sound and is directly determined by frequency. High frequency → high pitch (shrill, like a flute). Low frequency → low pitch (deep, like a bass drum). Amplitude determines loudness (volume). Timbre (quality) determines the character of sound from different instruments at the same pitch.
📚 Formula Sheet — PC05
🌍 Wave Basics
v = fλ (wave equation)
f = 1/T
Sound in air ≈ 340 m/s at 25°C
Speed: solid > liquid > gas
Sound needs medium; light doesn't
🎵 Sound Properties
Pitch depends on frequency
Loudness depends on amplitude
Quality/timbre: waveform shape
Human hearing: 20–20,000 Hz
Ultrasound: >20,000 Hz
🏼 Echo
Min distance for echo: 17 m
Min time gap: 0.1 s
Distance = v×t/2 (SONAR)
Reverberation: multiple reflections
SONAR: ultrasound for depth finding
🚨 Doppler Effect
Source approaching → freq increases
Source moving away → freq decreases
Train whistle: higher as approaching
Red-shift: galaxy moving away
Blue-shift: source approaching
⚡ Quick Revision — PC05
🌍 Wave Types
Transverse: particle ⊥ propagation (light)
Longitudinal: particle ∥ propagation (sound)
v = fλ (always)
Sound: 340 m/s in air
Light: 3×10⁸ m/s in vacuum
🚨 Key Facts
Echo: min 17 m, min 0.1 s
Faster in solid, slower in gas
Sound needs medium, light doesn't
Ultrasound: SONAR, medical imaging
Infrasound: earthquakes, <20 Hz
🎵 Sound Characteristics
Pitch ↔ frequency
Loudness ↔ amplitude
Quality ↔ waveform (timbre)
Doppler: approaching → higher pitch
Doppler: receding → lower pitch
📝 Practice Exercise
E-01
A sound wave has frequency 500 Hz and speed 340 m/s. Its wavelength is:
(a) 0.68 m
(b) 1.7 m
(c) 6.8 m
(d) 0.34 m
E-02
Which range of sound cannot be heard by humans?
(a) 20–2000 Hz
(b) 200–2000 Hz
(c) >20,000 Hz (ultrasound)
(d) 1000–5000 Hz
E-03
A ship sends a sonar pulse and receives the echo after 4 seconds. Speed of sound in water = 1500 m/s. Depth of ocean at that point is:
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