Frequency Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Frequency.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The number of complete wave cycles that pass a fixed point per second, measured in hertz (Hz).

How many times something vibrates per second—high frequency means very rapid vibration.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Frequency and period are reciprocals — doubling the frequency halves the period.

Common stuck point: Hertz (Hz) means 'cycles per second'—it's a rate of repetition, not a total count.

Sense of Study hint: When solving a frequency problem, check whether you are given the period or the wave speed and wavelength. If given the period T, use f = 1/T. If given speed v and wavelength \lambda, use f = v/\lambda. Always express your answer in hertz (Hz).

Worked Examples

Example 1

easy
A pendulum completes 20 swings in 40 \text{ s}. What is its frequency and period?

Solution

  1. 1
    Use the definition of frequency: cycles per second.
  2. 2
    Frequency: f = \frac{\text{number of cycles}}{\text{time}} = \frac{20}{40} = 0.5 \text{ Hz}
  3. 3
    Period: T = \frac{1}{f} = \frac{1}{0.5} = 2 \text{ s}

Answer

f = 0.5 \text{ Hz}, \quad T = 2 \text{ s}
Frequency is the number of complete oscillations per second, measured in hertz (Hz). Period is the time for one complete oscillation and is the reciprocal of frequency.

Example 2

medium
A radio station broadcasts at 100 \text{ MHz}. What is the wavelength of the radio wave? Use c = 3 \times 10^8 \text{ m/s}.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A wave has a period of 0.02 \text{ s}. What is its frequency?

Example 2

medium
A guitar string vibrates at a fundamental frequency of 330 \text{ Hz}. What are the frequencies of the second and third harmonics? If the string length is 0.65 \text{ m}, what is the wavelength of the fundamental?
← Back to Frequency Formula Explained Practice Mode

Related Concepts

WavesWavelengthPeriod

Background Knowledge

These ideas may be useful before you work through the harder examples.

waves