## How To Measure Frequency

A digital multimeter that includes a frequency counter mode can measure the frequency of ac signals and may also offer the following:

- MIN/MAX recording, which permits frequency measurements to be recorded over a specified period or the same way voltage, current or resistance measurements are recorded.
- Auto-range, which automatically selects the frequency range, except when the measured voltage is outside the frequency measurement range.

Power grids vary by nation. In the US, the grid is based on a highly stable 60-hertz signal, meaning it cycles 60 times per second.

In the US, household electrical power is based on a single-phase, 120-volt ac power supply. Power measured at a wall outlet in a US home will yield sine waves that oscillate between ±170 volts, with the true-rms voltage measuring at 120 volts. The rate of oscillation will be 60 cycles per second.

Hertz is named after German physicist Heinrich Hertz , first to broadcast and receive radio waves. Radio waves travel at one cycle per second .

Reference: Digital Multimeter Principles by Glen A. Mazur, American Technical Publishers.

## Relationship Between Frequency And Period

The frequency and period of a wave are *inversely* related to each other, and you only need to know one of them to work out the other. So if youve successfully measured or found the frequency of a wave, you can calculate the period and vice-versa.

The two mathematical relationships are:

Where *f* is frequency and *T* is period. In words, the frequency is the reciprocal of the period and the period is the reciprocal of the frequency. A low frequency means a longer period, and a higher frequency means a shorter period.

To calculate either the frequency or the period, then, you just do 1 over whichever quantity you already know, and then the result will be the other quantity.

## How Is Frequency Expressed

Frequency is usually expressed in the hertz unit, abbreviated Hz. One kilohertz is 1,000 Hz, and one megahertz is 1,000,000 Hz. In spectroscopy, another unit of frequency that is sometimes used is the wavenumber, the number of waves in a unit of distance.

**frequency**, in physics, the number of waves that pass a fixed point in unit time also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion. A body in periodic motion is said to have undergone one cycle or one vibration after passing through a series of events or positions and returning to its original state. *See also*angular velocity simple harmonic motion.

If the period, or time interval, required to complete one cycle or vibration is 1/2 second, the frequency is 2 per second if the period is 1/100 of an hour, the frequency is 100 per hour. In general, the frequency is the reciprocal of the period, or time interval i.e., frequency = 1/period = 1/. The frequency with which the Moon revolves around Earth is slightly more than 12 cycles per year. The frequency of the A string of a violin is 440 vibrations or cycles per second.

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## Natural Frequency Vs Forced Frequency

Natural frequencies are different from **forced frequencies**, which occur by applying force to an object at a specific rate. The forced frequency can occur at a frequency that is the same as or different from the natural frequency.

- When the forced frequency is not equal to the natural frequency, the amplitude of the resulting wave is small.
- When the forced frequency equals the natural frequency, the system is said to experience resonance: the amplitude of the resulting wave is large compared to other frequencies.

## Period Frequency And Amplitude: Definitions

Period, frequency, and amplitude are important properties of waves. As we mentioned before, the amplitude is related to the energy of a wave.

The **amplitude** is the maximum displacement from the equilibrium position in an oscillation

The period is the time taken for one oscillation cycle. The frequency is defined as the reciprocal of the period. It refers to how many cycles it completes in a certain amount of time.

The**period**is the time taken for one oscillation cycle.

The **frequency**describes how many oscillation cycles a system completes in a certain amount of time.

For example, a large period implies a small frequency.

$$f=\frac1T$$

Where \is the frequency in hertz, \,and\is the period in seconds, \.

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## What Are Amplitude Frequency And Period

The amplitude is the maximum displacement from the equilibrium position in an oscillation. It is an important property that is related to the energy of a wave. The period is the time taken for one oscillation cycle. The frequency is defined as the inverse of the period. It refers to how many cycles it completes in a certain amount of time.

## How Can A Bridge Collapse Due To Resonance

Read more about sound resonance and parallel resonance and learn how it is valid in practical life only through BYJUS engaging videos.

Put your understanding of this concept to test by answering a few MCQs. Click Start Quiz to begin!

Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz

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## Relation Between Frequency And Wavelength

Content Writer| Updated On -Dec 21, 2022

**Relation between Frequency and Wavelength can be shown by the following formula, **** = cf.**

Where,

- = wavelength of the
**wave** - C = speed of the wave in the given medium
- f = frequency of the wave

In a medium, energy is carried by a disturbance or by a vibration called a wave without a net movement of particles in that medium. Waves are crucial for the transfer of energy and it follows a periodic motion.

- Frequency can be defined as the number of cycles or turns that are made per second by an alternating quantity.
- Period can be expressed as the reciprocal of the frequency and vice versa.
- While, a Wavelength is the distance between each repeated wave in both the case of Longitudinal and
**Transverse waves**.

**Key Terms: Waves, Wavelength, Frequency, Amplitude, Energy, Temperature, Magnetic Intensity, Transverse Waves, Longitudinal Waves**

## Relationship Between Period Frequency And Amplitude

The period, frequency, and amplitude are all related in the sense that they are all necessary to accurately describe the oscillatory motion of a system. As we will see in the next section, these quantities appear in the trigonometric equation that describes the position of an oscillating mass. It is important to note that the amplitude is not affected by a wave’s period or frequency.

It is easy to see the relationship between the period, frequency, and amplitude in a Position vs. Time graph. To find the amplitude from a graph, we plot the position of the object in simple harmonic motion as a function of time. We look for the peak values of distance to find the amplitude. To find the frequency, we first need to get the period of the cycle. To do so, we find the time it takes to complete one oscillation cycle. This can be done by looking at the time between two consecutive peaks or troughs. After we find the period, we take its inverse to determine the frequency.

Displacement as a function of time for simple harmonic motion to illustrate the amplitude and period. Distance from \ to \ is the amplitude, while the time from \ to \ is the period, StudySmarter Originals

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## Frequency Time Period And Angular Frequency

As we know, many forms of energy like light and sound travel in waves. A wave is defined through various characteristics like frequency, amplitude and speed. In wave mechanics, any given wave enfolds parameters like frequency, time period, wavelength, amplitude etc. This article lets us understand and learn in detail about frequency, time period, and angular frequency.

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## Frequency Definition In Science

- Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
- B.A., Physics and Mathematics, Hastings College

In the most general sense, frequency is defined as the number of times an event occurs per unit of time. In physics and chemistry, the term frequency is most often applied to waves, including light, sound, and radio. Frequency is the number of times a point on a wave passes a fixed reference point in one second.

The period or duration of time of a cycle of a wave is the reciprocal of frequency. The SI unit for frequency is the Hertz , which is equivalent to the older unit cycles per second . Frequency is also known as cycles per second or temporal frequency. The usual symbols for frequency are the Latin letter *f* or the Greek letter .

## Waves Amplitude And Frequency

In physics, frequency is a property of a wave, which consists of a series of peaks and valleys. A waves frequency refers to the number of times a point on a wave passes a fixed reference point per second.

Other terms are associated with waves, including amplitude. A waves amplitude refers to the height of those peaks and valleys, measured from the middle of the wave to the maximum point of a peak. A wave with a higher amplitude has a higher intensity. This has a number of practical applications. For example, a sound wave with a higher amplitude will be perceived as louder.

Thus, an object that is vibrating at its natural frequency will have a characteristic frequency and amplitude, among other properties.

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## Key Takeaways: Natural Frequency

- Natural frequency is the rate at which an object vibrates when it is disturbed.
- Simple harmonic oscillators can be used to model the natural frequency of an object.
- Natural frequencies are different from forced frequencies, which occur by applying force to an object at a specific rate.
- When the forced frequency equals the natural frequency, the system is said to experience resonance.

## 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 – 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 – 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=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,

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

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

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.

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

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## Example Of Natural Frequency: Child On A Swing

A child sitting on a swing that is pushed and then left alone will first swing back and forth a certain number of times within a specific timeframe. During this time, the swing is moving at its natural frequency.

To keep the child swinging freely, they must be pushed at just the right time. These right times should correspond to the natural frequency of the swing to make the swing experience resonance, or yield the best response. The swing receives a little more energy with each push.

## Period Frequency And Amplitude Of Trigonometric Functions

Trigonometric functions are used to model waves and oscillations. This is because oscillations are things with periodicity, so they are related to the geometric shape of the circle. Cosine and sine functions are defined based on the circle, so we use these equations to find the amplitude and period of a trigonometric function.

$$y=a\ c\mathrm\left$$

The amplitude will be given by the magnitude of \.

$$\mathrm=\left|a\right|$$

The period will be given by the equation below.

$$\mathrm=\frac$$

The expression for the position as a function of the time of an object in simple harmonic motion is given by the following equation.

$$x=A\cos\left$$

Where \ is the amplitude in meters, \, and \ is time in seconds,\.

From this equation, we can determine the amplitude and period of the wave.

$$\mathrm=\left|A\right|$$

$$\mathrm=\fracT}\right|}=T$$

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## Period Frequency And Amplitude: Examples

To visualize these concepts experimentally, imagine you and your friend grabbing a rope by the ends and shaking it up and down such that you create a wave that travels through the rope. Let’s say that in one second, the rope completed two cycles. The frequency of the wave would be \. The period would be the inverse of the frequency, so the period of the wave would be half a second, meaning it would take half a second to complete one oscillation cycle.

A student observing an oscillating block counts \. Determine its frequency and period.

$$f=45.5\ }\min}\times\frac1}=0.758\ }}$$

$$f=0.758\ \mathrm$$

$$T=\frac1f=\frac1}=1.32\ \mathrm s$$

The period for an object oscillating in simple harmonic motion is related to the**angular frequency**of the object’s motion. The expression for the angular frequency will depend on the type of object that is undergoing the simple harmonic motion.

$$\omega=2\pi f$$

$$T=\frac\omega$$

Where \ is the angular frequency in radians per second, \.

The two most common ways to prove this are the pendulum and the mass on a spring experiments.

The**period of a spring** is given by the equation below.

$$T_s=2\pi\sqrt$$

Where \is the mass of the object at the end of the spring in kilograms, \, and \is the spring constant that measures the stiffness of the spring in newtons per meter, \.

A block of mass \ is attached to a spring whose spring constant is \. Calculate the frequency and period of the oscillations of this springblock system.

$$T_p=2\pi\sqrt$$

## Period Frequency And Amplitude

- The period is the time taken for one oscillation cycle.
- The frequency is defined as the inverse of the period. It refers to how many cycles it completes in a certain amount of time, \.
- The period of an object oscillating in simple harmonic motion is related to theangular frequencyof the object’s motion, \ and \.
- The amplitude is the maximum displacement from the equilibrium position in an oscillation. It is an important property that is related to the energy of a wave. The amplitude is not affected by a wave’s period or frequency. There can be two waves with the same frequency, but with different amplitudes.
- Trigonometric functions are used to model waves and oscillations, so we use these equations to find the amplitude and period, \\). To determine the amplitude, \. To determine the period, \.

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## Temperature Relation Between A Planet And Its Star

The black-body law may be used to estimate the temperature of a planet orbiting the Sun.

The temperature of a planet depends on several factors:

- Incident radiation from its star
- Emitted radiation of the planet
- The albedo effect causing a fraction of light to be reflected by the planet
- The greenhouse effect for planets with an atmosphere
- Energy generated internally by a planet itself due to radioactive decay, tidal heating, and adiabatic contraction due to cooling.

The analysis only considers the Sun’s heat for a planet in a Solar System.

The StefanBoltzmann law gives the total power that the Sun emits:

- P

- }=254.356\ \mathrm }

or 18.8 °C.

This is the temperature of the Earth if it radiated as a perfect black body in the infrared, assuming an unchanging albedo and ignoring greenhouse effects . The Earth in fact radiates not quite as a perfect black body in the infrared which will raise the estimated temperature a few degrees above the effective temperature. If we wish to estimate what the temperature of the Earth would be if it had no atmosphere, then we could take the albedo and emissivity of the Moon as a good estimate. The albedo and emissivity of the Moon are about 0.1054 and 0.95 respectively, yielding an estimated temperature of about 1.36 °C.