343
m/s
439.74359
Hz
0.439744
kHz
0.000439744
MHz
0.0022740525
s
2,762.990462
rad/s
8.055365778
rad/m
343
m/s
439.74359
Hz
0.439744
kHz
0.000439744
MHz
0.0022740525
s
2,762.990462
rad/s
8.055365778
rad/m
The Frequency Calculator computes the frequency of a wave from its wavelength and propagation speed using the relationship $$f = \frac{v}{\lambda}$$. Frequency describes how many complete oscillations a wave completes per second, measured in hertz (Hz). This calculator also provides the period, angular frequency, and wave number — all essential parameters in wave physics.
Frequency is central to nearly every branch of physics and engineering. In acoustics, frequency determines musical pitch — concert A is defined as exactly 440 Hz. In telecommunications, radio stations are identified by their broadcast frequency. In optics, the frequency of light determines its color, from red (approximately $$4.3 \times 10^{14}$$ Hz) to violet ($$7.5 \times 10^{14}$$ Hz).
The angular frequency $$\omega = 2\pi f$$ appears throughout physics in expressions for simple harmonic motion, AC circuits, and quantum mechanics. The period $$T = 1/f$$ gives the time duration of a single oscillation, which is critical for timing applications and signal processing.
The frequency is derived from the fundamental wave equation:
$$f = \frac{v}{\lambda}$$
where $$v$$ is the wave speed and $$\lambda$$ is the wavelength. For electromagnetic waves in vacuum, $$v = c = 299{,}792{,}458$$ m/s.
The calculator derives additional quantities:
These are connected by the dispersion relation $$\omega = vk$$, which holds for non-dispersive media where wave speed is independent of frequency.
The frequency value tells you how rapidly the wave oscillates. Higher frequencies correspond to shorter wavelengths and, for electromagnetic waves, higher photon energies. Human hearing spans roughly 20 Hz to 20 kHz. Visible light frequencies are around $$4 \times 10^{14}$$ to $$8 \times 10^{14}$$ Hz. The period is useful for understanding timing — a 1 MHz signal has a period of 1 microsecond.
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An FM radio wave with a 3-meter wavelength has a frequency of approximately 100 MHz, which is in the standard FM broadcast band (88–108 MHz).
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Medical ultrasound at 5 MHz in soft tissue (v ≈ 1540 m/s) has a wavelength of about 0.31 mm, providing good resolution for diagnostic imaging.
Frequency and period are reciprocals: $$f = 1/T$$ and $$T = 1/f$$. If a wave completes 100 cycles per second (100 Hz), each cycle takes 1/100 = 0.01 seconds. This inverse relationship means doubling the frequency halves the period.
Angular frequency $$\omega = 2\pi f$$ measures oscillation rate in radians per second. It appears naturally in equations involving circular or sinusoidal motion: $$x(t) = A\sin(\omega t + \phi)$$. It simplifies many physics and engineering formulas, especially in AC circuit analysis and quantum mechanics.
No. Frequency is determined by the source and remains constant as a wave passes between media. When a wave enters a medium with different speed, it is the wavelength that changes according to $$\lambda = v/f$$. This is why light changes color in a prism — different frequencies refract differently, but each frequency itself is unchanged.
Visible light spans approximately $$4.3 \times 10^{14}$$ Hz (red, ~700 nm) to $$7.5 \times 10^{14}$$ Hz (violet, ~400 nm). This narrow band is a tiny fraction of the electromagnetic spectrum, which extends from below 1 Hz (extremely low frequency radio) to above $$10^{24}$$ Hz (gamma rays).
Common conversions: 1 kHz = 1,000 Hz; 1 MHz = 1,000,000 Hz; 1 GHz = 10⁹ Hz; 1 THz = 10¹² Hz. For example, a 2.4 GHz Wi-Fi signal oscillates at 2,400,000,000 cycles per second.
A dispersion relation describes how frequency depends on wave number: $$\omega(k)$$. In non-dispersive media, $$\omega = vk$$ (linear), so all frequencies travel at the same speed. In dispersive media (like glass for light), $$v$$ depends on frequency, causing phenomena like prismatic rainbows and pulse broadening in optical fibers.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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