Concept To Remember

Introduction To Wavesequationsinusoidal And Speed Of 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 non-periodic waves:

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.