13.2 Wave Properties: Speed, Amplitude, Frequency, and Period

Learning Objectives

• Define amplitude, frequency, period, wavelength, and velocity of a wave.
• Relate wave frequency, period, wavelength, and velocity.
• Solve problems involving wave properties.

Key Terms

• Wavelength: Distance between adjacent identical parts of a wave.
• Wave Velocity: Speed at which the disturbance moves.

Wave Variables

• Amplitude: Maximum displacement from the equilibrium position.
  • For waves, it's the distance between the resting position and the maximum displacement.
• Frequency: Number of waves passing a point per second (Hz).
• Period: Time it takes for one wave cycle to complete.

Key Relationships

• Frequency and period are inverses:
  • ( f = \frac{1}{T} )
  • ( T = \frac{1}{f} )
• Wave velocity ( v_w ):
  • ( v_w = \lambda \times f )
  • Wavelength ( \lambda ) is the distance a wave has traveled during one period.

Understanding Waves

• Wave velocity is sometimes called propagation velocity.
• In a medium with constant ( v_w ), higher frequency means smaller wavelength.
• Example with sound: Low-frequency sound has a longer wavelength than high-frequency sound.

Practical Application: Waves in a Bowl

• Experiment to measure amplitude and period of waves produced by a cork.
• Variables like drop height can affect amplitude but not wavelength.

Geology and Seismic Waves

• Seismic waves include surface disturbances and pressure waves (P-waves) and shear waves (S-waves).
• P-waves travel faster and can pass through liquids, unlike S-waves.

Solving Wave Problems

• Worked Example: Calculate wave velocity given wavelength and period.
  • E.g., if wavelength is 10 m and period is 5 s, ( v_w = 2 \text{ m/s} ).

Practice Problem Concepts

• Frequency is the inverse of the period.
• Velocity can be found using frequency and wavelength.

Check Your Understanding

• Amplitude and wavelength definitions.
• Frequency expression in terms of period.
• Conditions for wavelength proportionality to period.

Additional Resources

• Videos and animations on amplitude, period, frequency, and wavelength.
• Seismic wave information related to geology and earthquake studies.