Time period frequency formula for frequency cycle duration periodic time period to angular frequency wavelength Hz to millisecond ms calculation calculate calculator Hz hertz to ms T to f worksheet definition amplitude

● Frequency formula − Conversion and calculation ●
Period, cycle duration, periodic time, time T to frequency f,
and frequency f to cycle duration or period T
− hertz to milliseconds − frequency to angular frequency

The only kind of periods meant by people who use this phrase are periods of time, so it's a redundancy. Simply say "time" or "period."

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Fill out the gray box above and click at the calculation bar of the respective column.

Frequency means oscillations (cycles) per second in Hz = hertz = 1/s.
1 second = 1000 ms and 1 ms = 0,001 seconds.

Simply enter the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

Oszilloscope: Input of the boxes (Div.) and timebase (Y) give the frequency.

Formula for period T

Physical value	symbol	unit	abbreviation	formula
Cycle duration	*T = 1 / f*	second	s	*T = λ / c*
Frequency	*f = 1 / T*	hertz	Hz = 1/s	*f = c / λ*
Wavelength	λ	meter	m	*λ = c / f*
Wave speed	c	meter per second	m/s	*c = λ × f*

Frequency formula

f = 1 / T and f = c / λ

Formulas and equations for frequency and wavelength

The formula for frequency is: f (frequency) = 1 / T (period).
The formula for time is: T (period) = 1 / f (frequency).

The formula for frequency is f (Hz) =
wave speed c (m/s) / wavelength λ (m).
The formula for wavelength is λ (m) =
wave speed c (m/s) / frequency f (Hz).

The unit hertz (Hz) was once called cps = cycles per second.

c = λ × f λ = c / f = c × T f = c / λ
Differentiate the Speed of the Medium:
Speed of Sound or Speed of Light

Choose: Speed of sound in air at a temperature of 20°C: c = 343 m/s
or speed of radio waves and light in a vacuum: c = 299,792,458 m/s.

The propagation speed of electrical signals via optical fiber is about 9/10
the speed of light, that is ≈ 270,000 km/s.
The propagation speed of electrical signals via copper cables is about 2/3
the speed of light, that is ≈ 200,000 km/s.

Speed of sound c = 343 m/s also equates to 1235 km/h, 767 mph, 1125 ft/s.

Changing the frequency does never change the amplitude and vice versa

The Angular frequency is ω = 2 π f

Given is the equation: y = 50 sin (5000 t)
Determine the frequency and amplitude.
Answer: The amplitude is 50 and ω = 5000.
So the frequency is f = 1/T = ω / 2 π = 795.77 Hz.

Simply enter the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

Conversion: Frequency to wavelength and vice versa

Sine wave or sinusoid and the period T

In physics and electrical engineering for the sinusoidal process is often used the
angular frequency ω instead of the frequency f. The speed or frequency of revolution
is a size at - preferably mechanical - rotating movements indicating the frequency
of revolutions. For example, it is an essential feature for engines. It will be given in
1/min, as revolutions per minute, or as in rpm.

y = sound pressure p (sound pressure amplitude).
If the graph shows at the x axis the time t, we see the period T = 1 / f.
If the graph shows at the x axis the distance d, we see the wavelength λ.
The largest deflection or elongation is referred to as amplitude a.
The amplitude has absolutely nothing to do with the frequency and wavelength.

● Wave Graphs ●

Waves may be graphed as a function of time or distance. A single frequency wave will appear as a sine wave in either case. From the distance graph the wavelength may be determined. From the time graph, the period and frequency can be obtained. From both together, the wave speed can be determined. Source:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/wavplt.html

In acoustics an expression for a sine wave is written in the form
y = A sin (2 π f T + φ). Where ω = 2 π f and A is the amplitude
and where f is the frequency of the wave measured in hertz.
Comparing the mathematical form y = A sin (B T + φ):
With this acoustical form we see that | B | = 2 π f. Hence we have
the frequency f = | B | / 2 π and the period T = 2 π / | B | = 1 / f.

Overtones, partials and harmonics from fundamental frequency

Keyboard, frequencies = Naming of musical notes, piano keys

Frequency domain of musical instruments and voices

SI multiples for hertz (Hz)
Value	Symbol	Name	Value	Symbol	Name
10⁻¹ Hz	dHz	decihertz	10¹ Hz	daHz	decahertz
10⁻² Hz	cHz	centihertz	10² Hz	hHz	hectohertz
10⁻³ Hz	mHz	millihertz	10³ Hz	kHz	kilohertz
10⁻⁶ Hz	µHz	microhertz	10⁶ Hz	MHz	megahertz
10⁻⁹ Hz	nHz	nanohertz	10⁹ Hz	GHz	gigahertz
10⁻¹² Hz	pHz	picohertz	10¹² Hz	THz	terahertz
10⁻¹⁵ Hz	fHz	femtohertz	10¹⁵ Hz	PHz	petahertz
10⁻¹⁸ Hz	aHz	attohertz	10¹⁸ Hz	EHz	exahertz
10⁻²¹ Hz	zHz	zeptohertz	10²¹ Hz	ZHz	zettahertz
10⁻²⁴ Hz	yHz	yoctohertz	10²⁴ Hz	YHz	yottahertz
Common prefixed units are in bold face.

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Frequency f: Hz	↔	Period T: ms
T = 1 / f f = 1 / T


Frequency f: Hz	↔	Angular Frequency ω: rad/s
ω = 2π × f f = ω / 2π