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. What is frequency and how is it measured in Hertz (Hz)?
Frequency is a fundamental property of a wave or oscillation that measures the number of complete cycles occurring in one second. The standard unit for frequency is the Hertz (Hz), named after the physicist Heinrich Hertz. One Hertz is equivalent to one cycle per second. The symbol commonly used for frequency is 'f' or sometimes the Greek letter nu (ν).
2. What is the relationship between frequency and time period?
Frequency and time period are inversely proportional to each other. The time period (T) is the time taken to complete one full cycle, while frequency (f) is the number of cycles per second. Their relationship is expressed by the formula: f = 1/T. This means if a wave has a high frequency, its time period will be very short, and vice versa.
3. What is the importance of frequency in sound waves?
In sound waves, frequency determines the pitch of the sound we hear. A higher frequency corresponds to a higher pitch (a more shrill sound), while a lower frequency corresponds to a lower pitch (a deeper, bass sound). The range of human hearing is typically between 20 Hz and 20,000 Hz (or 20 kHz).
4. What is the difference between frequency and wavelength?
Frequency and wavelength describe different aspects of a wave and are inversely related.
- Frequency (f) is a temporal measurement; it counts the number of wave cycles that pass a specific point per unit of time (usually one second). Its unit is Hertz (Hz).
- Wavelength (λ) is a spatial measurement; it is the distance over which the wave's shape repeats, for example, the distance between two consecutive crests. Its unit is metres (m).
5. How is the concept of frequency used beyond sound waves, for example, in light or electricity?
The concept of frequency is critical across many areas of physics and technology. Key examples include:
- Electromagnetic Waves: The frequency of light determines its colour and energy. Red light has a lower frequency than blue light. Beyond visible light, frequency defines different types of radiation like radio waves, microwaves, and X-rays.
- Alternating Current (AC) Electricity: In households, AC electricity reverses its direction at a standard frequency, which is 50 Hz in India and many other countries. This consistency is vital for designing compatible appliances.
- Computer Processors (CPUs): A processor's speed is measured in gigahertz (GHz), which indicates billions of processing cycles per second that the CPU can execute.
6. Does the frequency of a wave change when it travels from one medium to another?
No, the frequency of a wave remains constant when it passes from one medium to another. Frequency is determined by the source of the wave and does not change with the medium. While the wave's speed and wavelength do change upon entering a new medium, the number of wave cycles arriving at the boundary must equal the number of cycles leaving it per second. This is why a beam of light, for instance, maintains its colour (which is dependent on frequency) when it travels from air into water.
