Wave Motion

Drop a pebble into a pond and watch the ripples spread outward. Pluck a guitar string and hear the sound it produces. These are examples of waves -- disturbances that transfer energy from one point to another without transferring matter.

Types of Waves

Transverse waves: The particles vibrate perpendicular to the direction of wave propagation. Examples: light waves, waves on a string, water surface waves.

Longitudinal waves: The particles vibrate parallel to the direction of wave propagation. Examples: sound waves, compression waves in a spring.

Mechanical waves need a medium (sound, water waves). Electromagnetic waves do not need a medium (light, radio waves).

Wave Parameters

• Amplitude (A): Maximum displacement from the mean position
• Wavelength (lambda): Distance between two consecutive points in the same phase (e.g., crest to crest)
• Frequency (f): Number of complete oscillations per second (unit: Hz)
• Time period (T): Time for one complete oscillation. T = 1/f
• Wave speed (v): Speed at which the wave propagates

The Wave Equation

v = f lambda

This fundamental equation connects wave speed, frequency, and wavelength.

Worked Example

A wave on a string has a frequency of 200 Hz and a wavelength of 1.5 m. Find the wave speed.

Solution:

• v = f lambda = 200 x 1.5 = 300 m/s

Superposition of Waves

When two waves meet at the same point, the resulting displacement is the sum of the individual displacements. This is the principle of superposition.

• Constructive interference: Waves in phase add up (louder sound, brighter light)
• Destructive interference: Waves out of phase cancel (silence, darkness)

Standing (Stationary) Waves

When two identical waves travel in opposite directions, they form standing waves. These have:

• Nodes: Points of zero displacement (no vibration)
• Antinodes: Points of maximum displacement

Standing waves are formed in musical instruments. For a string fixed at both ends:

Frequency of nth harmonic: fn = n v / (2L)

where L is the length of the string and n = 1, 2, 3, ...

Real-World Connection

The sarangi and madal, traditional Nepali musical instruments, produce sound through standing waves on strings and membranes. The pitch depends on string length, tension, and mass per unit length.

Key Takeaways

• Waves transfer energy, not matter
• v = f lambda is the fundamental wave equation
• Superposition leads to interference (constructive or destructive)
• Standing waves form nodes and antinodes