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 non-periodic waves:

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

• Example: Sine waves.

• Non-periodic 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.