Frequency Formula

The Formula

f = \frac{1}{T} (frequency = 1 divided by period)

When to use: How many times something vibrates per second—high frequency means very rapid vibration.

Quick Example

Middle C on a piano vibrates at 262 Hz, meaning 262 complete cycles per second.

Notation

f is frequency in hertz (Hz = s^{-1}), T is the period in seconds, \omega (omega) is the angular frequency in rad/s, v is the wave speed in m/s, and \lambda (lambda) is the wavelength in metres.

What This Formula Means

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.

Formal View

Frequency is defined as f = \frac{1}{T} = \frac{\omega}{2\pi}, where T is the period and \omega is the angular frequency. For a travelling wave, f = v / \lambda.

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}.

Common Mistakes

  • Confusing frequency with period — frequency is cycles per second, period is seconds per cycle; they are reciprocals, not the same thing.
  • Forgetting to convert units: using milliseconds for period without converting to seconds before taking the reciprocal.
  • Thinking that higher frequency means faster wave speed — in a given medium, changing frequency changes wavelength, not speed.

Why This Formula Matters

Determines the pitch of sound, the color of visible light, and the energy of photons.

Frequently Asked Questions

What is the Frequency formula?

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

How do you use the Frequency formula?

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

What do the symbols mean in the Frequency formula?

f is frequency in hertz (Hz = s^{-1}), T is the period in seconds, \omega (omega) is the angular frequency in rad/s, v is the wave speed in m/s, and \lambda (lambda) is the wavelength in metres.

Why is the Frequency formula important in Physics?

Determines the pitch of sound, the color of visible light, and the energy of photons.

What do students get wrong about Frequency?

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

What should I learn before the Frequency formula?

Before studying the Frequency formula, you should understand: waves.

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Related Concepts

WavesWavelengthPeriod