Wave Motion and Types of Waves

Wave Motion

• Wave motion transfers energy without transferring matter. Examples include mechanical waves and electromagnetic radiation. Matter transfer, in contrast, involves energy transfer with movement of matter.
• Mechanical waves require: a source of disturbance, a medium for disturbance, and a mechanism for elements of the medium to affect each other.
• A pulse is a single disturbance that propagates through a medium (e.g., a flicked string). Its height and speed remain generally constant as it travels.

Types of Waves

• Transverse waves: The disturbance moves perpendicular to the direction of propagation. An example is a pulse on a string. In this case, each segment of the string moves at right angles to the pulse's path.
  • Example: In Figure 16.2, elements of the string (labeled P) move up and down (perpendicular), while the pulse travels horizontally.
• Longitudinal waves: The disturbance moves parallel to the direction of propagation.
  • Example: A pulse down a stretched spring (Figure 16.3), where the coils compress and expand parallel to the pulse direction.
  • Sound waves are longitudinal waves, characterized by pressure variations (high-pressure/low-pressure regions) traveling through a medium (e.g., air).

Pulse Representation

• A pulse's shape at any time t can be described by a mathematical function, y(x, 0) = f(x).

• The function y(x, t) represents the transverse position of any medium element at position x and time t.

• The shape of the pulse remains constant as it travels. If a pulse travels to the right, its position at time t is given by:

   y(x, t) = f(x - vt)
  

• If a pulse travels to the left, the position is:

   y(x, t) = f(x + vt)
  

• Wave function y(x, t) describes the position (y-coordinate) of any point (x-coordinate) on the medium at any time t.

• The function y(x) defines the pulse's shape at a fixed moment in time.

Earthquake Waves

• Earthquakes generate both transverse (S waves) and longitudinal (P waves) waves.
• P waves travel faster (7-8 km/s near the surface) and arrive first at a seismograph.
• S waves travel slower (4-5 km/s near the surface).
• Determining the time difference in arrival times of P and S waves at seismographs allows calculating the distance to the earthquake's epicenter.
• Combining data from multiple observation stations helps locate the exact earthquake origin.