Frequency, as used in physics, refers to the number of waves that can pass at a fixed point in a given period. For instance, if a wave takes ½ a second to pass through a certain point, the frequency of that wave is 2 per second. It can either be in the form of radio frequencies that work in the form of radio waves, or even the difference in light frequencies. Frequency is responsible for music, sound, and color variations.
Key Terms Relating to Frequency in Physics
When working with frequency, there are several terms and concepts that you will encounter. Here is a breakdown of those terms:
- Oscillation: Occurs when a wave moves back and forth regularly and repeatedly. The repeating variations are along the point of equilibrium. Oscillation is a harmonic and periodic motion. Frequency can also be described as the number of oscillations per unit of time.
- Cycle: A cycle occurs when an oscillating particle switches direction to its original point when moving from a certain point in a specific order. This usually happens from a stable equilibrium position to maximum displacement and back to the stable equilibrium.
- Wavelength: Wavelength is the distance between two successive crests. Frequency and wavelength are inversely proportional. The higher the frequency of any signal, the shorter the wavelength.
- Period: The period is the time a wave takes to make one complete oscillation. In Longitudinal waves, the period is the interval between two waves, and for a transverse wave, it is the time the wave takes to complete an entire cycle from the trough, crest, then back to the trough.
- Resonance: The universe is constantly in motion, even though most people don’t see it that way. For solid objects, this motion comes in the form of vibrations. The resonant frequency is the natural frequency in which the object vibrates at the maximum amplitude. It is witnessed in objects in equilibrium with acting forces and can vibrate longer under perfect conditions.
- Wave Motion: This harmonic motion carries energy from one place to another without moving matter. The wave frequency does not change when a wave travels from one medium to another.
- Interference: Interference occurs when unwanted radio waves on the same frequency collide, disrupting your device’s signal. It can affect reception or the equipment’s sound and picture quality.
- Diffraction: Diffraction is bending waves through obstacles and solid objects. You can propagate any form of energy through waves. Lightwave diffraction has more practical applications in modern technology, like holograms. Higher frequencies have a shorter wavelength making them more susceptible to edge diffraction.
- Doppler Effect: The Doppler effect occurs when there is a change in the wave frequency of the source when the wave moves with respect toward and past a stationary observer. The moving sound sends out sound waves at constant frequencies.
- Transverse Wave: A transverse wave is a wave whose vibration motion is perpendicular to the direction in which the wave is moving. They usually have a high frequency with many crests passing by the point.
The Frequency Formula
In physics, there are different frequency formulas that can be used to calculate the frequency of a wave or oscillation, depending on the known variables.
Formula 1: The formula for frequency in terms of time is given as:
Frequency (f) = number of cycles (N) ÷ time (T)
Frequency is measured in units of hertz (Hz), which represent the number of cycles per second. For example, if a vibrating object completes 10 cycles in 2 seconds, the frequency would be:
Frequency (f) = 10 cycles ÷ 2 seconds = 5 Hz
Formula 2: The formula for frequency in terms of wave speed and wavelength is given as:
Frequency (f) = wave speed (𝜈) ÷ wavelength (λ)
Formula 3: The formula for frequency in terms of angular frequency is given as:
f = angular frequency (ω)/2π
How Does Frequency Work?
To understand frequency well, let us examine how it works. Here is how frequency works in various contexts.
Harmonic Motion & Energy
Harmonic motion occurs when there’s a periodic vibration, like that of a violin string, in which the motions are symmetrical to the point of equilibrium. This type of vibration can either have one frequency and amplitude or be a combination of different components called harmonics.
Harmonic motion is also called periodic motion. Oscillation and wave motion can be used as perfect examples of harmonic motion.
Period and Frequency
A period is directly related to frequency. For a transverse wave, the period is the time taken to make one complete oscillation. For a longitudinal wave, the period is the interval between two successive waves. This value is expressed in seconds.
Frequency is the number of cycles per second in an oscillation and the number of waves passing through a given point per second in a wave motion. They are called Hertz, denoted by ’Hz.’ Higher frequencies are expressed in KiloHertz (KHz), representing 1000 cycles per second.
Wave motion is harmonic and can be used to carry energy. The energy is propagated from one place to another without moving any matter.
It is the number of vibrations made per second by any medium particles, since the frequency of a wave depends on the source producing the wave motion. This allows the wave to travel from one medium to another without changing the frequency.
The maximum displacement of any particle of the medium from its equilibrium position represents the amplitude of a wave. The wave amplitude is inversely proportional to the frequency.
The amplitude decreases as the frequency increases and vice versa. A short wavelength produces a high frequency with a higher pitch because it has quicker cycles.
Kinetic & Potential Energy
Harmonic and periodic motion typically involve energy that may be continuously converted from one form to another. Potential and kinetic energy are the two energies involved, with kinetic energy being due to movement and potential energy being due to its position and potential of movement.
Potential-kinetic conversions happen when an object is a reasonable distance from its stable equilibrium point, and there is some force capable of moving it; that is, potential energy. When the object starts moving towards equilibrium, this potential energy is now converted to kinetic energy.
To vibrate simply means to move back and forth in place. Vibration relates to oscillation because some vibrations are produced when an object oscillates.
For a molecule, all matter vibrates, and these vibrations are called natural frequencies. Natural frequency depends on the matter’s shape, composition, and size. A good example is how sound waves can shatter glass so long as they reach their natural frequency.
Oscillation is a type of harmonious movement that periodically takes place in one or more dimensions. Oscillations are of two types, spring and pendulum oscillations. With both, the object faces a disturbance, prompting it to swing back and forth from stable equilibrium. A spring oscillates along a straight path, while a pendulum does so along an arc.
Oscillation involves a predetermined cycle in which the spring or pendulum will always follow. It mainly involves the oscillating particle moving from one point to another and back to the original point in a direction that keeps reversing.
In context, the cycle shows movement from the stable equilibrium point to another point of maximum displacement. The stable equilibrium point is in the middle of the cycle, and two points of maximum displacement are at the highest and lowest points for the spring or highest points on each pendulum side.
How Is Frequency Measured?
We measure frequency in several ways. The methods have different accuracies, and while some are simple, others require specialized equipment. Let’s take a look at some of them.
Counting frequency is one of the simplest methods, so long as you follow the proper steps. There are three ways you can count frequency. The first one involves counting the zero crossings of a period, and is straightforward for one second. If you still need to, you must make some mathematical adjustments.
For instance, a half-second period requires you to multiply your count by two, whereas a 10-second period will prompt you to divide the count by 10. This method is easy, but as the frequency lowers, you count for longer, and the time base has to be exact to get correct readings.
For the second method, we accurately measure the period of a complete cycle. However, for this method to be effective, you have to make an exact measurement of the period.
For the third method, we use a known reference clock with the frequency to be measured while counting. This method can be done without a precise timebase and will, thus, guarantee you the best results. Additionally, the reference clock can effectively provide good resolution at both high and low frequencies.
Using a Stroboscope
A stroboscope also goes by the name strobe light or strobe tachometer. A strobe tachometer can measure the revolution speed and frequency of vibrating and moving parts, components, and appliances.
You can adjust the flash frequency of its light pulse depending on the measured parameters, making the readings more accurate. Since stroboscopes emit light pulses at different frequencies, they can provide frequency readings.
To measure the frequency using a stroboscope, you need to adjust the frequency until the wheel stops, indicating that only one light pulse is emitted in each complete wheel rotation.
All you need to do now is read the frequency reading on the stroboscope, which will equal the frequency you are measuring. This method is handy in plants where you can find worn-out equipment like belts, springs, and valves using a stroboscope light.
By Frequency Counter
A frequency counter measures the number of oscillation cycles of any electromagnetic signal. You can directly read out these pulses per second after measurement. So, how exactly does a frequency countermeasure frequency?
Most use a counter that counts events within a specific time interval. You will then transfer this value to the display, and the count will return to zero.
Suppose the event in question stably repeats itself but with a lower frequency than the clock oscillator used. In that case, the resolution of the final measurement has to be improved differently. Rather than counting the number of cycles occurring in a predetermined time frame, you will use the time needed for an entire set of cycles.
For the best results, the timebase has to be carefully calibrated as it is the internal oscillator generating the time signals. All you have to do for electronic signals is read the interface to the instrument, where you will get your reading.
Regarding accuracy, a frequency counter’s reading dramatically relies on the stability of its time base.
The heterodyne method is one of the most accurate frequency-measuring methods. In this method, we use the counter to calculate the square wave of the beat signal. An analog-digital converter (ADC) and computer work as the counter.
The sin wave beat signal will then be reconfigured and converted to a digital signal using the ADC. Afterward, the computer analyzes this digital signal, and the digital signal processor calculates the frequency.
This frequency measurement method works best with multi-channel signals and displays real-time results. Regarding accuracy, heterodyne methods are more accurate than traditional methods.
Real-life Applications of Frequency
Several devices and appliances work using the frequency concept. Let us look at some of these real-life applications of frequency.
The grandfather clock, invented by Christiaan Huygens (1629-1695), dramatically uses the pendulum concept. The frequency of a pendulum equals the number of swings per minute. You get the frequency when you divide the square root of acceleration due to gravity with the pendulum’s length.
This relationship allows one to adjust the length of pendulums in the clock, effectively changing its frequency. If the pendulum is short, the clock will run faster; a long pendulum results in a slowly running clock. This is how a grandfather clock works, with a pendulum controlling the second, minute, and hour hands.
A metronome is an instrument used for calculating the tempo and speed of music. This instrument dates back to the 19th century and uses a pendulum.
The pendulum is attached to a sliding weight on top and a fixed weight at the bottom. There also is a numbered scale that shows frequency. To alter the beat, you move the upper weight, which instantly changes the speed and tempo of the music.
When an object is put into resonant vibrations at the natural frequency, the vibrations come in a manner that forms a standing wave pattern in the object. Some examples of these objects include a guitar string, a Chladni plate, or a trombone air column. Each one of the natural frequencies produced by an object has its vibrational mode pattern.
Harmonic frequencies are the specific frequencies where these patterns are created in the different objects. At other frequencies, the disturbance produced by a medium is usually irregular.
Music instruments rely significantly on this concept as they vibrate regularly and periodically, with their harmonic frequencies related to each other through whole number ratios. This relation between harmonic frequencies results in the pleasant music these instruments produce.
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