Frequency cycle per second hertz Hz duration amplitude period periodic time to angular frequency formulary acoustic equation wavelength formula conversion relationship frequency worksheet t=1/f definition - sengpielaudio
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Frequency  formulaConversion and calculation
Period, cycle duration, periodic time, time T to frequency f,
and frequency f  to cycle duration or period T T = 1 / f and f = 1 / T
hertz to milliseconds and 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."
Tuning fork

 Frequency f  Hz   |  Period T  ms 
Period T  ms   |   Frequency f  Hz 

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 = 1 s = 1000 ms | 1 ms = 0.001 s | 1 µs = 0.000001 s
cps = cycles per second

Note line

To use the calculator, simply enter a value.
The calculator works in both directions of the

Period = Time
Frequency f  
 ↔  Period T  
T = 1 / f                              f = 1 / T

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

 Centimeters per period / div.  cm 
Timebase Y  ms 
Frequency f = 1/T  Hz 

Formula for period (cycle duration) 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 und f = c / λ

Time conversion - As time goes by

Formulas and equations for frequency and wavelength

The formula for frequency is: f (frequency) = 1 / T (period).
f = c / λ = wave speed c (m/s) / wavelength λ (m).
The formula for time is: T (period) = 1 /
f (frequency).
The formula for wavelength is
λ (m) = c / f
λ = c / f = 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.

 There are four parts to a wave:
wavelength, period, frequency, and amplitude

Changing the frequency (hertz, Hz) does never change the amplitude and vice versa
Sine curve

The Angular Frequency is ω = 2π × f

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

To use the calculator, simply enter a value.
The calculator works in both directions of the

Frequency f
 ↔  Angular Frequency ω
ω = 2π × f                              f = ω / 2π

Conversion: Frequency to wavelength and vice versa

Sinusoidal curve

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.

Wavelength and period
The y axis shows the 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 ...
also nothing with the wavelength.

● Wave Graphs ●
Waves may be graphed as a function of time or distance. A single frequency
wave will appear as a sine wave (sinosoid) 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:

Amplitude Time Distance
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
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.

A typical question: What is the relationship between wavelength, temperature, and frequency?

Explain the relationship between distance, time, and frequency in determining
wavelength or: What is the equation with frequency, distance, and time?

Speed = distance / time
Speed = wavelength × frequency
Wavelength × frequency = distance / time
Wavelength = distance / (time × frequency)

Rainbow Line

Masterclock calculator (clock rate)

To use the calculator, simply enter a value.
The calculator works in both directions of the

Reference wordclock 48.0 kHz 
Piano tuning
Reference frequency 440 Hz 
Studio wordclock
Reference wordclock 44.1 kHz 
Piano tuning f 
Reference frequency 440 Hz 
Studio wordclock

Rainbow Line

Calculator with reference frequency

 Reference wordclock   kHz 
Reference frequency   Hz
Piano tuning f   Hz
Studio wordclock fs   kHz
Interval deviation   cent

For downward tuning the reference frequency and piano tuning can be changed.
100 cent is equivalent to a semitone (halftone).

Note names: English and German System by comparison
Calculations of Harmonics from Fundamental Frequency

Rainbow Line

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