Frequency (Hz)

Dhristi JEE 2022-24

What is Frequency?

In our daily life, there are many events that repeat after regular intervals of time. In physics, we have learnt about some motions that are also repeating after a regular interval of time. These types of motions are called periodic motion. The examples of periodic motions are vibration of tuning fork, oscillation of simple pendulum, rotation of earth etc. The frequency of a periodic motion is defined as the number of times the motion is repeated in one second. We will learn about the frequency in detail and we will also discuss how to calculate the frequency of various period motion.


Frequency- Definition and Unit

In a period motion, the motion repeats after a regular interval of time and the number of periodic motions completed per unit time is called frequency. The time taken to complete one periodic motion is called time period. The examples of periodic motions are simple pendulum, vibration of particles in a wave, vibration of tuning fork etc. The unit of frequency is Hz. The Hz full form is Hertz which is named after German physicist Heinrich Hertz. He proved the existence of electromagnetic waves. The dimension of frequency is [T-1]. For example, The frequency of a vibrating tuning fork is marked as 526 Hz meaning the tuning fork is vibrating 526 times per second. 


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Frequency and Time Period 

The frequency of a period motion can also be defined as the reciprocal of time period. Therefore, the relationship between frequency and time period of a periodic motion is given by,

\[f =\frac{1}{T}\]

Where,

f - Frequency of the periodic motion.

T - Time period of the periodic motion


Examples
:

1. The time period of a period motion is 100 seconds. Find the frequency of the periodic motion.

Ans:

The time period of the motion =T=100 s

The relation between frequency and the time period of the periodic motion is given by the formula,

\[f =\frac{1}{T}\]

Where,

f - Frequency of the periodic motion.

T - Time period of the periodic motion.

Substitute the value of time period in the above equation to calculate the frequency.

⇒ \[f =\frac{1}{T}\]

\[f=\frac{1}{100s}\]

f=0.01 Hz

Therefore, the frequency of the periodic motion is 0.01 Hz

2. A particle is undergoing circular motion and takes 20 seconds to complete the circular path four times. Find the frequency of the motion of  the particle.

Ans:

The motion of a particle in a circular path is a periodic motion. First we have to find time period given by the formula,

\[T=\frac{\text{Time taken to complete the given revolutions}}{\text{No of revolution}}\]

Substitute the values given in the above equation to obtain the time period.

\[T=\frac{\text{Time taken to complete the given revolutions}}{\text{No of revolution}}\]

\[T = \frac{20s}{4}\]

T=5 s

Now, we have to calculate frequency using time period given by the formula,

\[f =\frac{1}{T}\]

Where,

f - Frequency of the periodic motion.

T - Time period of the periodic motion

Substitute the value of time period in the above equation to obtain the frequency.

\[f =\frac{1}{T}\]

\[f =\frac{1}{5}\]

f=0.2 Hz

Therefore, the circular motion of the particle has 0.2 hertz frequency.


Frequency of a Wave


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Frequency of a wave is defined as the number of cycles per second. In a transverse wave, one cycle comprises one crest and trough. For a longitudinal wave, one cycle comprises one compression and rarefaction. For example, the frequency of a sound wave is 1000 Hz meaning the sound wave is completing 1000 cycles per second.

For a transverse wave, wavelength of a wave is the distance between two consecutive crests or two consecutive troughs. For a longitudinal wave, wavelength is defined as the distance between two consecutive compression or two consecutive troughs. The frequency, wavelength, and speed of a wave are related by the formula given by,

𝑣 = fλ
Where,

f - frequency of the wave.

𝑣 - speed of the wave

λ - wavelength of the wave.

Example:

1. A wave is traveling with a speed of 340 m/s in a medium. The wavelength of the wave is given as 5 m. Find the frequency of the wave.

Ans

The speed of the  wave travelling in a medium =𝑣  =340 m/s

The wavelength of the wave λ =5 m

The formula to calculate the frequency of the wave is given by,

𝑣 = fλ

Substitute the values for speed of the wave and the wavelength of the wave in the above formula and simplify to calculate the frequency of the wave.

​𝑣  = fλ

340 m/s=f x 5 m

⇒ \[f = \frac{340 m/s}{5m}\]

f= 68 Hz

Therefore, the frequency of the wave is calculated as 68 Hz

2. The frequency of a wave traveling with a speed of 200 m/s is 100 Hz. Find the distance between the two consecutive crests of the wave.

Ans

The frequency of the wave = f =100 Hz

The speed of the wave =​𝑣  =200 m/s

The distance between two consecutive crests of the wave is equal to the wavelength of the wave. So, we have to calculate the wavelength of the wave. The frequency, wavelength, and speed of a wave are related by the formula given by,

​𝑣 = fλ

Where,

f - frequency of the wave.

​𝑣 - speed of the wave

λ - wavelength of the wave.

Substitute the values for frequency and speed of the wave in the above formula and simplify to calculate the wavelength.

​𝑣 =fλ

200 m/s=100 Hz x λ

\[\lambda = \frac{200 m/s}{100Hz}\]

λ = 2 m

The wavelength of the wave is obtained as 2 m. Therefore, the distance between the two consecutive crests is 2 m.

Conclusion

The frequency of a periodic motion is equal to the reciprocal of the time period. So, we can obtain the frequency if the time period is given. The frequency is expressed as Hz. The Hz full form is hertz. 1 hertz is equal to one cycle per second .For a wave, frequency is the number of cycles per second. We have also seen the formula relating the frequency, wavelength and speed of a wave.  

FAQs on Frequency (Hz)

1. Define the frequency of a wave.

Ans:

The frequency of a wave is defined as the number of cycles per second. One cycle of the wave means one crests and one trough for a transverse wave and one compression and one rarefaction of a longitudinal wave. The formula to calculate the frequency of the wave is given by,


\[Frequency = \frac{\text{number of cycles}}{\text{time taken}}\]


Hertz is a unit of measurement of frequency. 1 hertz is equal to one cycle of the wave completed in one second.

2. What is the relationship between frequency and time period?

Ans:

The time period of a periodic motion is equal to the reciprocal of the frequency. The relationship between time period and frequency is given by the formula,


\[f =\frac{1}{T}\]


Where,

f - Frequency of the periodic motion.

T - Time period of the periodic motion

We can calculate the frequency of the periodic motion using the above formula if the time period is given and vice versa.

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