Waves are fundamental to physics, describing the propagation of energy through a medium or vacuum. In competitive exams like JEE, a solid grasp of key wave properties is crucial for solving problems in mechanics (mechanical waves) and electromagnetism (electromagnetic waves). This module will break down wave speed, frequency, wavelength, and amplitude, providing the foundational knowledge needed for mastery.

Wave speed is the distance a wave crest or trough travels per unit of time. It's a measure of how quickly the disturbance propagates through the medium. For mechanical waves, speed depends on the properties of the medium (like tension and density for a string, or bulk modulus and density for sound waves). For electromagnetic waves, speed in a vacuum is a universal constant, the speed of light (c).

Frequency is the number of complete wave cycles (oscillations) that pass a given point per unit of time. It is typically measured in Hertz (Hz), where 1 Hz equals one cycle per second. Frequency is an intrinsic property of the wave source and does not change when the wave moves from one medium to another.

Wavelength is the spatial period of the wave, meaning it is the distance over which the wave's shape repeats. It is the distance between two consecutive corresponding points of the same phase, such as two adjacent crests or troughs. Wavelength is measured in units of length, typically meters (m).

Amplitude is the maximum displacement or magnitude of oscillation of a point on the wave from its equilibrium position. It represents the 'height' of a wave crest or the 'depth' of a wave trough. Amplitude is related to the energy carried by the wave; a larger amplitude means more energy.

The core equation connecting wave speed, frequency, and wavelength is:

$v = f \lambda$

This equation is a cornerstone for solving wave problems. It implies that if you know any two of these quantities, you can calculate the third. Remember that frequency is determined by the source, while speed is determined by the medium. Therefore, when a wave enters a new medium, its speed and wavelength change, but its frequency remains constant.

Consider a sound wave with a frequency of 440 Hz (middle C) traveling through air at a speed of 343 m/s. We can calculate its wavelength using the formula $\lambda = v/f$. Therefore, $\lambda = 343 \text{ m/s} / 440 \text{ Hz} \approx 0.78 \text{ m}$. This means that each cycle of this sound wave occupies about 0.78 meters of space in the air.