# Frequency Formula

The frequency formula is used to find the frequency of a wave. Frequency is defined as the number of cycles completed per unit time. It also tells about how many crests go through a fixed point per unit time. Sometimes it is known as reciprocal of time. Frequency is expressed in Hertz(Hz). The frequency formula is used to find the frequency of the wave. Let us understand it better using solved examples.

## What is the Frequency Formula?

Frequency is the total number of occurrences of a repeating event per unit of the given time. There are different frequency formulas to calculate frequency depending upon the quantities known. The formula for the frequency of a wave is used to find frequency (f), time period (T), wave speed (V), and wavelength (λ). 1 Hertz refers to one cycle per second.

### Frequency Formula

The frequency formula is given as,

**Formula 1: **The frequency formula in terms of time is given as:

f = 1/T

### where,

- f is the frequency in hertz measured in m/s, and
- T is the time to complete one cycle in seconds

**Formula 2: **The frequency formula in terms of wavelength and wave speed is given as,

f = 𝜈/λ

where,

- 𝜈 is the wave speed in m/s, and
- λ is the wavelength of the wave in m

**Formula 3:** Frequency in terms of angular frequency is articulated as,

f = ω/2π

where ω is the angular frequency

Let us understand the frequency formula better through a few solved examples.

## Examples Using Frequency Formula

**Example 1: **Using the frequency formula, find the frequency of a wave where one cycle is completed in 0.5s.

**Solution: **

To find: Frequency

Given:

Time = 0.5s

Using frequency formula

f = 1 / T

f = 1 / 0.5

f = 2

**Answer: Frequency is 2Hz.**

**Example 2: **Find the frequency of lightwave when the wavelength of the light is 600nm.

**Solution: **

To find: Frequency

Given: Wavelength = 600nm = 600 × 10^{-9} m

= 6 × 10^{-7 }m

We know that the speed of the light = 3 × 10^{8 }m/s

Using frequency formula

f = 𝜈 / λ

f = 3 ×10^{8} / 6 ×10^{-7}

f = 5 ×10^{14 }sec^{-1}

**Answer: Frequency is 5 ×10 ^{14} Hz. **

**Example 3: **Determine the frequency of the pendulum that takes 4 seconds to complete one cycle.

**Solution: **

To find: Frequency

Given:

Time = 4s

Using frequency formula

f = 1 / T

f = 1 / 4

f = 0.25

**Answer: Frequency is 0.25 Hz.**

## FAQs on Frequency

### What is Frequency Formula?

The frequency formula is defined as the formula to find the frequency of the wave. The frequency formula is used to find frequency (f), time period (T), wave speed (V), and wavelength (λ).

### What are the Applications of Frequency Formula?

The applications of the frequency formula:

- The frequency is considered an important parameter in the fields of science and engineering and so does the frequency formula.
- The formula for frequency is used to specify the rate of oscillatory and vibratory phenomena, mainly the mechanical vibrations, the audio signals (sound), the radio waves, and the light waves.
- The frequency formula is used to determine the frequency (f), time period (T), wave speed (V), and wavelength (λ) and to derive the other related formulas.

### How is Frequency Formula Applied For the Given values?

The percentage formula is given as,

- The frequency formula in terms of time is given as: f = 1/T where, f is the frequency in hertz, and T is the time to complete one cycle in seconds
- The frequency formula in terms of wavelength and wave speed is given as, f = 𝜈/λ where, 𝜈 is the wave speed, and λ is the wavelength of the wave
- The frequency formula in terms of angular frequency is given as, f = ω/2π where ω is the angular frequency

### What is 'T' in Frequency Formula?

In the frequency formula, f = 1/T, T is the time period. T refers to the time to complete one cycle (in seconds). Time period is inversely proportional to the frequency.

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