Topic 7

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Topic 7 — Key Facts for DU Admission (Bangladesh) Core concept: Waves and Sound — properties of wave motion and acoustic phenomena High-yield point: Wave equation, resonance, Doppler effect formulas ⚡ Exam tip: At least one numerical problem from wave equation or Doppler effect appears in every DU admission test

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Topic 7 — DU Admission (Bangladesh) Study Guide Overview: Waves and Sound is a high-scoring physics topic requiring conceptual clarity Core principles: Wave properties, sound propagation, acoustic phenomena Key points: Wave equation v = fλ, Doppler effect, resonance frequency Study strategy: Learn formulas with conditions of application, solve 5–10 problems daily

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Waves and Sound — Complete Study Notes

Introduction to Waves

A wave is a disturbance that transfers energy through a medium without transferring matter. Understanding wave behavior is essential for optics, acoustics, and modern physics — all areas tested in the DU admission exam.

Types of Waves

1. Mechanical Waves

Require a material medium for propagation:

• Transverse waves: Particles vibrate perpendicular to wave direction (light, waves on string)
• Longitudinal waves: Particles vibrate parallel to wave direction (sound waves)

2. Electromagnetic Waves

Do NOT require a medium — can travel through vacuum:

• Include light, radio waves, X-rays, gamma rays
• All travel at speed of light: c = 3 × 10⁸ m/s

3. Matter Waves

Associated with moving particles (de Broglie hypothesis) — introduced in modern physics sections.

Important Wave Quantities

Symbol	Quantity	Unit	Formula
v	Wave velocity	m/s
f	Frequency	Hz
λ	Wavelength	m
T	Time period	s	T = 1/f
A	Amplitude	m

The Wave Equation

v = f × λ

This is the most important equation in wave physics. It connects all three fundamental wave properties.

Example problem: A wave travels at 340 m/s with frequency 512 Hz. Find its wavelength.

• λ = v/f = 340/512 = 0.664 m

Alternate form: v = λ/T (since T = 1/f)

Wave Properties

Reflection

• Waves bounce back when they hit a boundary
• Angle of incidence = Angle of reflection
• Used in echo, sonar, optical fibers

Refraction

• Wave changes direction when passing into a different medium
• Frequency remains constant; wavelength and speed change
• v ∝ √(elastic property/inertial property)

Diffraction

• Bending of waves around obstacles
• Most noticeable when obstacle size ≈ wavelength
• Explains sound traveling around corners

Interference

• Two or more waves combine in the same region
• Constructive interference: Crest meets crest → resultant amplitude maximum
• Destructive interference: Crest meets trough → resultant amplitude minimum
• Condition for constructive: path difference = nλ
• Condition for destructive: path difference = (2n+1)λ/2

Polarization

• Confines vibration to one plane
• Only transverse waves can be polarized
• Applications: Polaroid sunglasses, 3D movies

Sound Waves

Sound is a longitudinal mechanical wave with frequency between 20 Hz and 20,000 Hz.

Type	Frequency Range
Infrasound	< 20 Hz
Audible sound	20 Hz – 20 kHz
Ultrasound	> 20 kHz

Speed of Sound

• In air: v ≈ 330 + 0.6T m/s (where T is temperature in °C)
• At 25°C: v ≈ 345 m/s
• In water: ~1500 m/s
• In steel: ~5000 m/s

Important: Speed of sound is independent of pressure and frequency (in ideal gases).

Propagation of Sound

Sound requires a material medium. It cannot travel through vacuum.

Speed in gases: v = √(γP/ρ) = √(γRT/M)

• γ (gamma) = ratio of specific heats (1.4 for air)
• P = pressure, ρ = density, M = molar mass
• v ∝ √(T) — speed increases with temperature
• v is independent of pressure (at constant temperature)
• v is independent of frequency

Characteristics of Sound

1. Pitch (Frequency): Higher frequency → Higher pitch
2. Loudness (Amplitude): Greater amplitude → Louder sound
3. Quality (Waveform): Determines timbre, distinguishes same pitch from different instruments

Intensity Level

β (in dB) = 10 log₁₀(I/I₀)

Where I₀ = 10⁻¹² W/m² (threshold of hearing)

• Increase of 10 dB = 10× intensity
• Increase of 20 dB = 100× intensity
• Increase of 30 dB = 1000× intensity

Echo and Reverberation

• Echo: Distinct reflected sound heard after original sound
• Minimum distance for echo in air: d = v × t/2 = 17.2 m (at 25°C, t = 0.1s)
• Reverberation: Persistence of sound due to multiple reflections (important in hall design)

Doppler Effect

When source and observer move relative to each other, apparent frequency changes.

Formula:

• Source moving, observer stationary: f’ = f × v/(v ∓ vₛ)
• Observer moving, source stationary: f’ = f × (v ± vₒ)/v

Sign convention:

• Source towards observer: use − in denominator (frequency increases)
• Observer towards source: use + in numerator (frequency increases)

Examples:

1. Ambulance siren: Higher pitch approaching, lower pitch receding
2. Train whistle: Same principle

Stationary Waves (Standing Waves)

Formed when two waves of same amplitude and frequency travel in opposite directions.

Closed Pipe (One end closed):

• Fundamental frequency: f₁ = v/4L
• Harmonics: fₙ = (2n-1)v/4L (only odd harmonics)
• Wavelength: λₙ = 4L/n

Open Pipe (Both ends open):

• Fundamental frequency: f₁ = v/2L
• Harmonics: fₙ = nv/2L (all harmonics)
• Wavelength: λₙ = 2L/n

Resonance

When frequency of applied force matches natural frequency of body, amplitude becomes maximum.

Examples:

• Breaking glass with high-pitched sound
• Bridge collapse due to wind matching natural frequency
• Microwave oven: microwave frequency matches water molecule frequency

Beats

Beats occur when two waves of slightly different frequencies interfere.

Beat frequency: f_beat = |f₁ - f₂|

This is used for tuning musical instruments.

Application in Music

Term	Definition
Note	Sound of specific frequency
Octave	Frequency doubles
Tone	Single frequency (pure note)
Noise	Random frequencies

Must-Remember Formulas

1. Wave equation: v = fλ
2. Doppler effect (source moving): f’ = f(v/(v ∓ vₛ))
3. Doppler effect (observer moving): f’ = f((v ± vₒ)/v)
4. Beat frequency: f_beat = |f₁ - f₂|
5. Sound intensity level: β = 10 log₁₀(I/I₀)
6. Closed pipe fundamental: f₁ = v/4L
7. Open pipe fundamental: f₁ = v/2L
8. Echo distance: d_min = 17.2 m (at 25°C)

Common DU Admission Questions

1. Wave equation numerical (find λ or f)
2. Doppler effect — source moving towards/away
3. Standing wave harmonics in open/closed pipe
4. Difference between transverse and longitudinal waves
5. Energy in wave vs amplitude relationship

Exam Tips

• For Doppler effect: Remember “towards increases, away decreases”
• In resonance tube problems, end correction e = 0.3d must be considered
• Light waves are transverse; all electromagnetic waves can be polarized
• Sound waves are longitudinal; cannot be polarized

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