Introduction To Wavesequationsinusoidal And Speed Of Waves
Concepts for understanding waves
Transverse and longitudinal waves:

Transverse waves: Particles vibrate perpendicular to the direction of the wave’s propagation.
 Example: Water waves.

Longitudinal waves: Particles vibrate parallel to the direction of the wave’s propagation.
 Example: Sound waves.
Periodic and nonperiodic waves:

Periodic waves: Waves that repeat their pattern at regular intervals.

Example: Sine waves.

Nonperiodic waves: Waves that do not repeat their pattern.

Example: Earthquakes.
Sine, cosine, and tangent functions:

Sine function: sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.

Cosine function: cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle.

Tangent function: tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. Amplitude, wavelength, and frequency:

Amplitude: The maximum displacement of a wave from its rest position.

Wavelength: The distance between two consecutive peaks or troughs of a wave.

Frequency: The number of waves that pass a fixed point in one second.
Wave equation: $$v=fλ$$
 The wave equation shows the relationship between the wave’s speed (v), frequency (f), and wavelength (λ).
Speed of waves: $$v=\sqrt{T/μ}$$
 The speed of a wave (v) is determined by the tension (T) in the string and the mass per unit length(μ).
Sinusoidal Waves

Phase difference: The difference in the phase of two waves at a given point, causing constructive or destructive interference.

Interference of waves: The combination of two or more waves that results in a new wave pattern.

Standing waves: Waves that appear to be stationary due to the interference of two waves of the same frequency and amplitude traveling in opposite directions.

Resonance: The condition in which the natural frequency of a system matches the frequency of an applied force, resulting in increased amplitude.
Speed of Waves

Wave speed in different media: The speed of waves varies depending on the medium through which they travel.

Example: Waves travel faster in solids than liquids and faster in liquids than gases.

Factors affecting wave speed: The speed of waves is influenced by factors such as temperature, density, and elasticity of the medium.

Doppler effect: The change in frequency of a wave due to the motion of the source or observer.

Example: The siren of a moving ambulance sounds higher in pitch as it approaches and lower in pitch as it recedes.