Frequency is the number of occurrences of a repeating event for each unit of the time given. There are various frequency equations to work out frequency relying on the quantities we know. We can find frequency (f), wave speed (v), time period (T), and wavelength (λ) by using the formula for the frequency of a wave. 1 Hertz refers to one cycle each second.

Frequency Formula

Generally, to find the frequency of a wave, a frequency formula is utilized. The number of cycles completed for each unit time is characterized as frequency. It likewise tells about the number of peaks that go through a fixed point for each unit time. It is also referred to as temporal frequency, which emphasizes the contrast between spatial frequency and angular frequency. It is reciprocal of time. The unit of frequency is Hertz. By using the frequency formula we can track down the frequency of the wave.

 

Frequency Formula

The frequency formula is given as,

• Relation between frequency, wavelength, and wave speed

The relation between frequency, wavelength, and wave speed is given as,

f = v/λ

Where, 

v is measured in  m/s and it is the wave speed 

λ is measured in  m and it is the wavelength of the wave

• Relation between frequency and time period

The relation between frequency and time period is given as:

f = 1/T  

Where,

f is measured in 1/s, the frequency in hertz 

T is measured ins s, the time period

Since frequency is inversely proportional to the time period. So, as the time period increases frequency will decrease.

• Relation between frequency and angular frequency

The relation between frequency and angular frequency is given as:

f = ω/2π

Where ω is the angular frequency

Since frequency is directly proportional to the time period. So, as the time period increases frequency will also increase. 

Sample Problems

Question 1: Find the frequency of a wave where one cycle of the wave is finished in 2s.

Solution:   

Given:

Time = 2s

Usingthe below formula,

f = 1 / T

f = 1 / 2

f = 0.5

Frequency is 0.5Hz.

Question 2: Find the frequency of lightwave when the wavelength of the light is 500nm.

Solution:   

Given: 

Wavelength = 500nm = 500 × 10^-9 m

= 5 × 10^-7 m

We know that the speed of the light = 3 × 10⁸ m/s

Using below formula,

f = v / λ

f = 3 × 10⁸ / 5 × 10^-7                                 

f = 6 × 10¹⁴ sec^-1

Frequency is 6 × 10¹⁴Hz.  
 

Question 3: Determine the frequency of the pendulum that takes 8 seconds to complete one cycle.  

Solution:

Given:

Time = 4s

Using below formula,

f = 1 / T

f = 1 / 8

f = 0.125

Frequency is 0.125 Hz.

Question 4: Find the angular velocity of the wave, if the frequency is 10hertz.

Solution:

Frequency = 10hertz

Using below formula

f = ω/2π

ω = 2πf

= 20π

Angular velocity is 20π

Question 5: Determine the time pendulum takes to complete one cycle if the frequency of the pendulum is 20hertz.

Solution:

Frequency = 20hertz

Using below formula

f = 1 / T,

T = 1 / f,

T = 1 / 20 ,

T = 0.05,

Time period is 0.05