Waves and Their Properties

Progressive Waves

• A progressive wave transfers energy from one place to another
• Examples include water waves (transverse) and sound waves (longitudinal)
• Energy transfer occurs in the same direction as the wave's movement
• Intensity (I) is directly proportional to the square of the amplitude (A) (I = kA²)
• Higher amplitude waves transmit more energy

Stationary Waves

• Formed by the superposition of two progressive waves (same type, equal frequency, and amplitude, traveling in opposite directions)
• Both longitudinal and transverse waves can form stationary waves
• When two coherent progressive waves overlap, a stationary wave is produced
• A common example is a stationary wave on a string produced by rapid oscillation

Velocity of a Wave on a String

• The velocity (v) of a wave on a string is given by the formula: v = √(T/μ)
  • v = velocity of wave (ms⁻¹)
  • T = tension in the string (N)
  • μ = mass per unit length of string (kgm⁻¹)

Fundamental Frequency of a Vibrating String

• Fundamental frequency (f₀) is the lowest frequency a vibrating string or pipe can produce
• f₀ = 1/2L √(T/μ)
• f₀ = fundamental frequency (Hz)
• L = length of string (m)
• T = tension in the string (N)
• μ = mass per unit length of the string (kg/m)

Nodes and Antinodes

• Nodes are points along a stationary wave where particles are at rest and displacement is zero
• Antinodes are points midway between nodes, where displacement is twice the amplitude of either progressive wave
• They are important in phenomena like Kundt's tube

Kundt's Tube

• Used to measure the speed of sound
• A long cylindrical tube, one end open, filled with powder
• A loudspeaker (connected to a signal generator) at the open end creates a stationary wave
• The powder collects at the displacement nodes, allowing wavelength to be calculated and speed (v=fλ) determined

Ultra Sound

• High-frequency sound waves (above 20,000 Hz)
• Medical applications (diagnosing fractures, measuring foetus size, cleaning equipment)
• Industrial uses (detecting hairline fractures, exploring Earth's structures)
• Navigation applications

Stationary Waves in Open Pipes

• Fundamental frequency (f₀): f₀ = (v/2L)
• Overtones/Harmonics are produced along with fundamental frequency

Stationary Waves in Closed Pipes

• Fundamental frequency: f₀ = (v/4L)
• Overtones/Harmonics are produced along with fundamental frequency

Resonance Tube

• Used to determine the speed of sound
• A tuning fork of known frequency is placed above a resonant air column
• The air column reflects the sound waves, producing stationary waves
• Resonance occurs when the fundamental mode of vibration matches the tuning fork frequency

Wavelength of Light Waves

• Visible light has a wavelength of 400-700 nanometers (nm)

Diffraction through a Single Slit

• When a parallel beam of light passes through a single slit, diffraction occurs, spreading out into a pattern on a screen
• This effect causes a spreading of light and is related to wavelength and slit width

Diffraction Grating

• A grating consists of a large number of parallel, equally spaced slits or lines
• Creates interference patterns of bright and dark fringes when monochromatic light is shone on it.
• dsinθ= nλ
• d is the slit separation
• θ is the angle of diffraction
• n is the order of the interference
• λ is the wavelength of the light.

Interference of Light Waves with Single and Double Slits

• Two or more waves overlap and create an interference pattern.
• Single or double slits show the constructive and destructive interference of waves of light

This quiz covers the concepts of progressive and stationary waves, including energy transfer and wave velocity on a string. Understand the relationship between amplitude and intensity, and explore how waves can form stationary patterns through superposition. Test your knowledge on these fundamental wave principles!