Show that frequency and time period of waves are inverse of each other.

Definition:

Frequency (f): The number of wave cycles per second.

Time Period (T): The time taken for one complete wave cycle.

From the wave equation:

f = 1/T

T = 1(f)

This means that frequency and time period are reciprocals of each other. If the frequency increases, the time period decreases, and vice versa.

Example: If a wave has a frequency of 5 Hz, its time period is:

T = {1}{5} = 0.2 seconds

Related Questions:

  1. What do you mean by oscillation? Define simple harmonic motion. What are the conditions for a body to perform SHM? Give examples of bodies that perform SHM.
  2. Show that a vibrating mass-spring system performs simple harmonic motion. What is its time period? On what factors does it depend?
  3. Explain the following terms for SHM: Vibration, amplitude, time period, frequency.
  4. Explain that a steel ball dropped from the edge of a shining bowl performs SHM.
  5. What is a simple pendulum? Show that a vibrating simple pendulum performs SHM. What is the formula for the time period of a simple pendulum? On what factors does it depend?
  6. Explain the process of damping. Differentiate between damped and undamped oscillations.
  7. Define the term wave. Explain it with the help of an example. Differentiate between mechanical waves and electromagnetic waves.
  8. Define transverse waves. Discuss its motion with the help of an example. Also define the following terms for transverse waves: Crest, Trough, Wavelength, Frequency, and Time Period.
  9. Define longitudinal waves. Discuss its motion with the help of an example. Also define the following terms for longitudinal waves: Rarefaction, Compression, Wavelength.
  10. Derive the formula for the speed of waves () relating speed, frequency, and wavelength.
  11. Simple harmonic motion and waves
  12. At the extreme position, velocity is zero but acceleration is maximum in simple harmonic motion. How can you theoretically explain it?
  13. What will happen to the acceleration of a mass-spring system if its mass is doubled?
  14. A simple pendulum has a time period “T”. What will happen to its time period if its thread length is shortened to half?
  15. A simple pendulum has a time period of 4 seconds. Will its time period remain the same or change if its steel bob is replaced by a wooden bob of the same size?
  16. Same masses are attached to different springs, one is vibrating faster. Why?
  17. A simple pendulum has a time period “T” in Murree. In Karachi, it has a different time period. What would you do to make its time period the same as it was in Murree?
  18. What will happen to the frequency of waves in a ripple tank if the time period of the electrical vibrator is decreased? What will happen to the wave speed?
  19. Why do water waves refract at the boundary of shallow water and deep water in a ripple tank experiment?
  20. Under what conditions are waves diffracted the most?