Waves are disturbances that transfer energy from one point to another without the permanent displacement of the medium through which they travel.

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CLASSIFICATION OF WAVES 

• Mechanical Waves: Require a medium (solid, liquid, or gas) to propagate. Examples include sound waves and waves on strings.
• Electromagnetic Waves: Do not require a medium and can travel through a vacuum. Examples include light waves and radio waves.
• Longitudinal Waves: The displacement of the medium is parallel to the direction of wave propagation (e.g., sound waves).
• Transverse Waves: The displacement of the medium is perpendicular to the direction of wave propagation (e.g., waves on a string).
• Progressive Waves: Waves that move through a medium, transferring energy.
• Stationary Waves: Formed by the interference of two waves travelling in opposite directions, resulting in nodes and antinodes.

15.1     EXAMPLES OF WAVES

• Springs: Compression and rarefaction waves in a spring.
• Ropes: Transverse waves created by shaking one end of a rope.
• Stretched Strings: Vibrations create standing waves.
• Ripple Tank: Demonstrates wave patterns and behaviour like reflection and refraction.

          15.2     CHARACTERISTICS OF WAVES

• Reflection: Bouncing back of waves when they hit a barrier.
• Refraction: Change in direction of waves as they pass from one medium to another.
• Diffraction: Spreading of waves when they pass through an opening or around obstacles.
• Plane Polarization: Orientation of waves in a single plane.

SUPERPOSITION OF WAVES (INTERFERENCE): When two or more waves overlap, they combine to form a new wave pattern. This can result in constructive or destructive interference.

BEATS: The phenomenon that occurs when two waves of slightly different frequencies interfere, resulting in a fluctuating amplitude.

DOPPLER EFFECT (QUALITATIVE TREATMENT): The change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source. It explains why a moving sound source (like a passing siren) sounds different as it approaches and then recedes.

DISTINCTION BETWEEN PARTICLE MOTION AND WAVE MOTION: Particle motion involves the movement of individual particles, while wave motion involves the propagation of energy through a medium.

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RELATIONSHIP BETWEEN FREQUENCY, WAVELENGTH, AND WAVE VELOCITY: The wave velocity (V) is related to frequency (f) and wavelength (λ) by the equation:

V = f * λ

PROGRESSIVE WAVE EQUATION: The equation for a progressive wave can be expressed as:

y (x, t) = A * sin(kx – ωt)

y (x, t) = A * sin(kx + ωt)

Where                 A is amplitude,

k is the wave number, and

ω is the angular frequency.

          15.3     SOUND WAVES

A sound wave is a longitudinal mechanical wave that travels through a medium (like air, water, or solids) as a pattern of pressure disturbances caused by the vibration of an object, carrying energy away from the source. 

NECESSITY FOR A MATERIAL MEDIUM IN SOUND WAVE

• Sound waves require a medium (solid, liquid, or gas) to travel through.
• They cannot propagate in a vacuum because there are no particles to transmit the vibrations.

SPEED OF SOUND IN SOLIDS, LIQUIDS, AND AIR

• Sound travels fastest in solids due to closely packed particles (e.g., steel ~ 5000 m/s).
• Sound travels slower in liquids than in solids (e.g., water ~ 1500 m/s).
• Sound travels slowest in gases (e.g., air ~ 343 m/s at room temperature).

CHARACTERISTICS OF SOUND WAVES

• Quality: The timbre or colour of the sound, which distinguishes different instruments.
• Pitch: The perceived frequency of a sound; higher frequencies correspond to higher pitches.
• Intensity: The power of the sound wave, related to its amplitude.
• Loudness: The human perception of sound intensity, which can vary based on frequency.

REFLECTION OF SOUND: When sound waves encounter a barrier, they bounce back, leading to phenomena such as echoes and reverberation.

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          15.4     ECHOES AND REVERBERATION

ECHO: A distinct reflection of sound heard after a delay. It is given by the formula:

                                                v = 2d/t

Where                 d = distance to the object (metres),

v = speed of sound (metres/second),

t = time for the echo to return (seconds).

APPLICATIONS OF ECHOES

• Used in sonar technology, navigation, and architectural acoustics.
• Echoes can help in locating objects (e.g., bats use echolocation).

REVERBERATION: The persistence of sound in a space due to multiple reflections. In application, reverberation is important in music and sound design to enhance audio experiences.

ADVANTAGES OF REVERBERATION: Reverberation can enrich sound quality in music.

DISADVANTAGES OF REVERBERATION: Excessive reverberation can lead to unclear sound in auditoriums.

          15.5     HARMONICS AND OVERTONES

When a string or air column vibrates, it produces a fundamental frequency and additional frequencies called harmonics or overtones.

Harmonics are simply integral multiples of the fundamental frequency. The term overtone is employed to ask any resonant frequency above the elemental frequency – and overtone may or might not be a harmonic.

RESONANCE: Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its resonant frequency, defined as the frequency that generates the maximum amplitude response in the system.

Simply, it occurs when an object vibrates at its natural frequency, amplifying sound (e.g., a tuning fork causing a glass to vibrate).

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          15.6     FREQUENCY OF A NOTE EMITTED BY AIR COLUMNS IN OPEN AND CLOSED PIPES

• Open pipes: Fundamental frequency is determined by the length of the pipe:

(f = v/2L)

• Closed pipes: The fundamental frequency is determined by the length and has a different relationship (f = v/4L).