Waves and Sound

Waves and Sound

1. Definition of a Wave

A wave is a disturbance that propagates energy from one place to the other without the transport of matter.

Waves are broadly of two types:

1. Mechanical Wave

2. Non-mechanical Wave

2. Mechanical Waves

The waves that require a material medium (solid, liquid, or gas) for their propagation are called mechanical waves or elastic waves.

Types of Mechanical Waves

(i) Longitudinal Wave

If the particles of the medium vibrate in the direction of propagation of the wave, the wave is called a longitudinal wave.

Examples:

• Waves on springs

• Sound waves in the air

(ii) Transverse Wave

If the particles of the medium vibrate perpendicular to the direction of propagation of the wave, the wave is called a transverse wave.

Examples:

• Waves on strings under tension

• Waves on the surface of water

Special Case:

• Waves produced by a moving motorboat on the surface of water are both transverse and longitudinal.

3. Non-mechanical Waves or Electromagnetic Waves

The waves that do not require a medium for their propagation, i.e., that can propagate even through a vacuum, are called non-mechanical waves.

Examples:

• Light

• Heat

In fact, all electromagnetic waves are non-mechanical.

• All electromagnetic waves consist of photons.

• The wavelength range of electromagnetic waves is 10⁻¹⁴ m to 10⁴ m.

Properties of Electromagnetic Waves

1. They are neutral (uncharged).

2. They propagate as transverse waves.

3. They propagate with the velocity of light.

4. They contain energy and momentum.

5. Their concept was introduced by Maxwell.

Waves that are not electromagnetic:

1. Cathode rays

2. Canal rays

3. β rays

4. α rays

5. Sound waves

6. Ultrasonic waves

4. Some Important Electromagnetic Waves

• Microwaves: Electromagnetic waves of wavelength range 10⁻³ m to 10⁻² m.

• In an electromagnetic wave, the electric field vector and the magnetic field vector vibrate perpendicular to each other and also perpendicular to the direction of propagation.

5. Basic Wave Concepts

Phase of Vibration

• The phase of vibration of a vibrating particle at any instant is the physical quantity that expresses the position as well as direction of motion of the particle at that instant with respect to its equilibrium (mean) position.

Amplitude

• Amplitude is defined as the maximum displacement of the vibrating particle on either side from the equilibrium position.

Wavelength

• Wavelength is the distance between any two nearest particles of the medium vibrating in the same phase. It is denoted by the Greek letter λ.

• In a transverse wave, the distance between two consecutive crests or troughs

• In a longitudinal wave, the distance between two consecutive compressions or rarefactions

Relation Between Wavelength, Frequency, and Velocity

Velocity of wave = frequency × wavelength, or v = nλ

• A path difference of Δx corresponds to a phase difference.

6. Sound Waves

Sound waves are longitudinal mechanical waves.

Types of Sound Waves

1. Audible or Sound Waves

• Frequency range: 20 Hz to 20,000 Hz

• Sensitive to the human ear

• Generated by vibrating bodies like a tuning fork, the vocal cords

2. Infrasonic Waves

• Frequency: less than 20 Hz

• Produced by earthquakes, volcanic eruptions, ocean waves, elephants, and whales

3. Ultrasonic Waves

• Frequency: greater than 20,000 Hz

• The human ear cannot detect ultrasonic waves; some animals, like bats, dogs, cats, and mosquitoes, can detect and produce them.

• Produced by Galton's whistle, Hartman's generator, quartz crystal vibrations (piezo-electric effect), ferromagnetic rod vibrations (magnetostriction)

Applications of Ultrasonic Waves

• Sending signals

• Measuring the depth of the sea

• Cleaning clothes, airplanes, and machinery

• Removing lamp soot from chimneys

• Sterilizing liquids

• Ultrasonography

7. Speed of Sound

Speed in Different Media

• Depends on the elasticity and density of the medium.

• Maximum in solids, minimum in gases

• Speed changes with medium, wavelength changes, and frequency remains constant.

• Independent of frequency

Effects on Speed of Sound

1. Pressure: No effect

2. Temperature: Increases with temperature; rises 0.61 m/s per 1°C

3. Humidity: More in humid air than in dry air

8. Characteristics of Sound Waves

1. Intensity: Energy passing per unit area per unit time; affects loudness (unit: bel, decibel, phon)

2. Pitch: Distinguishes sharp/shrill sounds from grave/dull; depends on frequency

3. Quality: Distinguishes sounds with the same intensity and pitch; depends on overtones

9. Echo

• Sound reflected from a rigid surface.

• Minimum distance for echo: 17 m (16.6 m)

• Persistence of ear: 1/10 sec

• Refraction makes sound travel farther at night

10. Resonance

If the frequency of the imposed periodic force equals the natural frequency, the body oscillates with a large amplitude.

11. Interference of Sound

• Superposition of two or more sound waves of the same frequency

• Constructive: same phase, maximum intensity

• Destructive: opposite phase, minimum intensity

12. Stationary Waves

• Two progressive waves (same type, amplitude, frequency, wavelength) travel in opposite directions

• Superimpose to form stationary or standing waves

13. Diffraction of Sound

• Sound deviates around obstacles comparable to the wavelength (~1 m)

14. Doppler’s Effect

• Apparent frequency changes if the source and observer move relative to each other

• Approaching: frequency increases

• Receding: frequency decreases

15. Mach Number

• Mach number = speed of source/speed of sound

• Mach > 1: supersonic

• Mach > 5: hypersonic

• Mach < 1: subsonic

16. Shock Waves

• A supersonic body produces a conical disturbance.

• Carries huge energy; may crack windows or damage buildings

17. Bow Waves

• A motorboat moving faster than sound produces bow waves on the water's surface

18. Reflection of Sound

• When sound reflects from a rigid boundary, compression returns as compression with no change in phase

Final Thoughts

A wave is a disturbance that transfers energy without moving matter and can be mechanical or non-mechanical. Mechanical waves need a medium and can be longitudinal (sound) or transverse (water or string waves), while non-mechanical waves like light and heat travel through a vacuum.

Sound waves are longitudinal and classified as audible, infrasonic, or ultrasonic, with ultrasonic waves used in medical imaging and cleaning. Wavelength, frequency, and velocity describe a wave, while phase and amplitude describe motion. The speed of sound depends on the medium, temperature, and humidity, being fastest in solids.

Phenomena like echo, resonance, interference, the Doppler effect, and shock waves are part of wave behavior. Understanding waves helps explain everyday sounds, communication, and advanced technologies.