Intro to waves

Introduction to Waves

What is a Wave

• A wave is defined as a disturbance that moves from its point of origin.

• Waves are associated with simple harmonic motions.

• The time taken to complete one full up and down movement of a wave is known as its time period.

• Frequency is defined as the number of events (or cycles) occurring in a unit of time.

Relationships and Equations

• Frequency (f) and time period (T) are inversely related to each other.
     - The relationship can be expressed mathematically as:
     $f = \frac{1}{T}$
  
  

Wave Anatomy

Key Concepts

• Wave Velocity: Also referred to as the speed of the wave, it is defined as the rate at which disturbances move through a medium.
     - Wave velocity can be calculated using the formula:
     $v = f \times \lambda$
     - Where:
       - $v$ = wave velocity (speed)
       - $f$ = frequency
       - $\lambda$ = wavelength

• The speed at which disturbances propagate is also known as propagation velocity.

• Changing the frequency or wavelength does NOT alter the wave speed in a fixed medium.

• Amplitude: This is the maximum displacement from the equilibrium position, measured from the equilibrium line to either the crest or the trough of the wave on a graph.

• The amplitude of a wave is independent of both the period and frequency of the wave.

• Wavelength: Can be measured only from position vs. position graphs (position graphs).

• Period and frequency: These values are inversely related for a constant wave velocity, and they can only be determined from position-time graphs.

Types of Waves

Mechanical Waves

• Definition: Mechanical waves require a medium to travel through, involving oscillating particles within the wave.

• Examples:
    - The ocean (water waves)
    - Earthquakes (seismic waves)
    - Strings (vibrating guitar strings)
    - Springs (compression waves)
    - Sound waves

Electromagnetic Waves

• Definition: Electromagnetic waves DO NOT require a medium to propagate.

• Examples:
    - Light waves
    - Infrared radiation
    - Radio signals

Wave Types Based on Propagation

Transverse Waves

• These waves have a disturbance that propagates perpendicular to the direction of propagation.

Longitudinal Waves

• These waves have a disturbance that propagates parallel to the direction of propagation.

Exit Ticket

• Example Calculation: Given that $f = 20 Hz$, we can derive the time period from the frequency:
     $T = \frac{1}{f} = \frac{1}{20} = 0.05 \text{ seconds}$

• Also, using the wave speed formula, if the wave velocity was 5 m/s, the wavelength would be calculated as:
     $\lambda = \frac{v}{f} = \frac{5 \, m/s}{20 \, Hz} = 0.25 \, m$

Wave Graph Labeling Exercise

• For the graph labeled "Position vs. Position (1)":
    - Amplitude
    - Crest
    - Trough
    - Wavelength
    - The graph cannot determine the time period (T) directly.
    - The graph cannot determine frequency (f) directly either.