Hertz to Wavelength Converter
Convert frequency to wavelength across different mediums with precise calculations
How to Convert Hertz to Wavelength
The relationship between frequency (measured in hertz) and wavelength is inversely proportional. When frequency increases, wavelength decreases, and vice versa. This relationship is defined by the wave equation that connects these two properties through the speed of propagation.
λ = c / f
Where:
λ (lambda) = Wavelength in meters
c = Speed of wave propagation in m/s
f = Frequency in Hertz
λ (lambda) = Wavelength in meters
c = Speed of wave propagation in m/s
f = Frequency in Hertz
Conversion Steps
- Identify the frequency value – Determine the frequency you want to convert, noting its unit (Hz, kHz, MHz, etc.)
- Convert to standard Hertz – If your frequency is in kHz, MHz, or GHz, convert it to Hz by multiplying by the appropriate factor
- Select the medium – Choose the appropriate wave speed based on the medium (light in vacuum, sound in air, etc.)
- Apply the formula – Divide the wave speed by the frequency: λ = c / f
- Convert to desired unit – Adjust the result to your preferred wavelength unit (meters, centimeters, nanometers, etc.)
Conversion Examples
Example 1: FM Radio Wave
Convert 100 MHz to wavelength in meters
• Frequency: 100 MHz = 100,000,000 Hz
• Speed: 299,792,458 m/s (light in vacuum)
• Calculation: λ = 299,792,458 / 100,000,000 = 2.998 m
• Result: 2.998 meters
Convert 100 MHz to wavelength in meters
• Frequency: 100 MHz = 100,000,000 Hz
• Speed: 299,792,458 m/s (light in vacuum)
• Calculation: λ = 299,792,458 / 100,000,000 = 2.998 m
• Result: 2.998 meters
Example 2: Red Light
Convert 430 THz to wavelength in nanometers
• Frequency: 430 THz = 430,000,000,000,000 Hz
• Speed: 299,792,458 m/s (light in vacuum)
• Calculation: λ = 299,792,458 / 430,000,000,000,000 = 6.972 × 10⁻⁷ m
• Result: 697 nanometers
Convert 430 THz to wavelength in nanometers
• Frequency: 430 THz = 430,000,000,000,000 Hz
• Speed: 299,792,458 m/s (light in vacuum)
• Calculation: λ = 299,792,458 / 430,000,000,000,000 = 6.972 × 10⁻⁷ m
• Result: 697 nanometers
Example 3: Audible Sound
Convert 440 Hz (musical note A4) to wavelength in air
• Frequency: 440 Hz
• Speed: 343.2 m/s (sound in air at 20°C)
• Calculation: λ = 343.2 / 440 = 0.78 m
• Result: 78 centimeters
Convert 440 Hz (musical note A4) to wavelength in air
• Frequency: 440 Hz
• Speed: 343.2 m/s (sound in air at 20°C)
• Calculation: λ = 343.2 / 440 = 0.78 m
• Result: 78 centimeters
Frequency to Wavelength Conversion Table
Electromagnetic Waves (Light in Vacuum)
| Frequency | Wavelength | Wave Type |
|---|---|---|
| 30 Hz | 10,000 km | Extremely Low Frequency (ELF) |
| 3 kHz | 100 km | Very Low Frequency (VLF) |
| 300 kHz | 1 km | Low Frequency (LF) |
| 3 MHz | 100 m | Medium Frequency (MF) |
| 30 MHz | 10 m | High Frequency (HF) |
| 300 MHz | 1 m | Very High Frequency (VHF) |
| 3 GHz | 10 cm | Super High Frequency (SHF) |
| 30 GHz | 1 cm | Extremely High Frequency (EHF) |
| 300 GHz | 1 mm | Microwave |
| 430 THz | 697 nm | Red Light |
| 540 THz | 555 nm | Green Light |
| 670 THz | 447 nm | Blue Light |
Sound Waves in Air (20°C)
| Frequency | Wavelength | Sound Type |
|---|---|---|
| 20 Hz | 17.16 m | Infrasound (lowest human hearing) |
| 100 Hz | 3.43 m | Low Bass |
| 440 Hz | 78 cm | A4 Musical Note |
| 1 kHz | 34.32 cm | Mid-Range Sound |
| 4 kHz | 8.58 cm | Human Voice Range |
| 10 kHz | 3.43 cm | High Frequency |
| 20 kHz | 1.72 cm | Ultrasound (highest human hearing) |
Electromagnetic Spectrum
The electromagnetic spectrum encompasses all types of electromagnetic radiation, from radio waves to gamma rays. Each region is characterized by a specific range of frequencies and corresponding wavelengths.
Radio Waves
Frequency: < 3 GHz
Wavelength: > 10 cm
Applications: Broadcasting, communication
Microwaves
Frequency: 3 GHz – 300 GHz
Wavelength: 1 mm – 10 cm
Applications: WiFi, radar, cooking
Infrared
Frequency: 300 GHz – 430 THz
Wavelength: 700 nm – 1 mm
Applications: Heat sensing, remote controls
Visible Light
Frequency: 430 – 750 THz
Wavelength: 400 – 700 nm
Applications: Human vision, photography
Ultraviolet
Frequency: 750 THz – 30 PHz
Wavelength: 10 – 400 nm
Applications: Sterilization, tanning
X-Rays
Frequency: 30 PHz – 30 EHz
Wavelength: 0.01 – 10 nm
Applications: Medical imaging
Gamma Rays
Frequency: > 30 EHz
Wavelength: < 0.01 nm
Applications: Cancer treatment, astronomy
Visible Light Spectrum
| Color | Wavelength Range | Frequency Range |
|---|---|---|
| Red | 622 – 780 nm | 384 – 482 THz |
| Orange | 597 – 622 nm | 482 – 503 THz |
| Yellow | 577 – 597 nm | 503 – 520 THz |
| Green | 492 – 577 nm | 520 – 610 THz |
| Blue | 455 – 492 nm | 610 – 659 THz |
| Violet | 390 – 455 nm | 659 – 769 THz |
Related Wave Conversions
Beyond converting hertz to wavelength, waves can be characterized and converted through several other related properties:
Frequency Conversions
- Hertz to Period – Convert frequency to the time duration of one complete wave cycle (T = 1/f)
- Hertz to Angular Frequency – Convert to radians per second (ω = 2πf)
- Hertz to Energy – Convert photon frequency to energy using Planck’s constant (E = hf)
- Hertz to RPM – Convert cyclical frequency to rotations per minute
Wavelength Conversions
- Wavelength to Frequency – Inverse conversion from wavelength back to hertz (f = c/λ)
- Wavelength to Wavenumber – Convert to reciprocal wavelength (k = 1/λ)
- Wavelength to Energy – Calculate photon energy from wavelength (E = hc/λ)
- Wavelength in Different Mediums – Adjust wavelength when waves pass through different materials
Note: When a wave travels from one medium to another, its frequency remains constant, but its wavelength and speed change according to the properties of the new medium. The refractive index determines how much the speed and wavelength are reduced.
Frequently Asked Questions
What is the relationship between hertz and wavelength?
Hertz (frequency) and wavelength have an inversely proportional relationship. As frequency increases, wavelength decreases, and vice versa. They are connected through the wave equation: λ = c/f, where c is the speed of wave propagation. This means higher frequency waves have shorter wavelengths.
Does wavelength change when a wave enters a different medium?
Yes, wavelength changes when a wave enters a different medium because the wave speed changes, but the frequency remains constant. For example, when light enters water from air, its speed decreases to about 75% of its vacuum speed, causing the wavelength to also decrease by the same proportion.
What is the wavelength of a 1 MHz radio wave?
A 1 MHz (1,000,000 Hz) radio wave traveling at the speed of light has a wavelength of approximately 300 meters. This is calculated using λ = c/f = 299,792,458 m/s ÷ 1,000,000 Hz ≈ 300 m. This frequency falls within the medium wave (MW) band used for AM radio broadcasting.
How do you convert GHz to wavelength in centimeters?
First, convert GHz to Hz by multiplying by 1 billion (10⁹). Then apply the formula λ = c/f using the speed of light (299,792,458 m/s). Finally, convert the result from meters to centimeters by multiplying by 100. For example, 2.4 GHz = 2.4 × 10⁹ Hz, giving λ = 0.1249 m = 12.49 cm.
What is the wavelength range of visible light?
Visible light ranges from approximately 390 nanometers (violet) to 780 nanometers (red). This corresponds to frequencies of about 769 THz (violet) down to 384 THz (red). Human eyes are most sensitive to green-yellow light around 555 nm, which has a frequency of approximately 540 THz.
Why is the speed of light used for electromagnetic wave conversions?
Electromagnetic waves, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, all travel at the speed of light in a vacuum (approximately 299,792,458 m/s). This universal constant makes it possible to calculate wavelength from frequency for any electromagnetic radiation using the same conversion factor.
How does temperature affect sound wave wavelength?
Temperature affects the speed of sound, which in turn affects wavelength (since frequency remains constant). In air, sound speed increases by about 0.6 m/s for each degree Celsius rise in temperature. At 20°C, sound travels at 343.2 m/s, while at 0°C it travels at 331.3 m/s. This means wavelengths are slightly longer at higher temperatures.
Can you convert wavelength back to frequency?
Yes, the conversion is reversible. To convert wavelength to frequency, use the formula f = c/λ, where f is frequency in hertz, c is the wave speed in the medium, and λ is wavelength in meters. Make sure all units are consistent before performing the calculation.
What is the wavelength of WiFi signals?
WiFi operates on two main frequency bands. The 2.4 GHz band has a wavelength of approximately 12.5 cm (125 mm), while the 5 GHz band has a wavelength of approximately 6 cm (60 mm). The newer WiFi 6E also uses the 6 GHz band with a wavelength of about 5 cm. These shorter wavelengths at higher frequencies allow for more data transmission but have reduced ability to penetrate walls.
Wave Properties & Physics
Waves are disturbances that transfer energy through space or matter. They exhibit several key properties that define their behavior and applications.
Core Wave Properties
Frequency (f)
Number of wave cycles per second
Measured in Hertz (Hz)
Remains constant across mediums
Wavelength (λ)
Distance between wave peaks
Measured in meters
Changes with medium density
Wave Speed (c)
Rate of wave propagation
Measured in m/s
Depends on medium properties
Period (T)
Time for one complete cycle
Measured in seconds
Reciprocal of frequency (T = 1/f)
Amplitude (A)
Maximum wave displacement
Related to energy/intensity
Independent of frequency
Energy (E)
Carried by wave motion
For photons: E = hf
Higher frequency = more energy
Wave Speed in Different Materials
| Medium | Sound Speed (m/s) | Light Speed (m/s) |
|---|---|---|
| Vacuum | N/A (requires medium) | 299,792,458 |
| Air (20°C) | 343 | ≈299,700,000 |
| Water (20°C) | 1,481 | 224,901,000 |
| Glass | 5,500 | 200,000,000 |
| Steel | 5,800 | N/A (opaque) |
| Diamond | 12,000 | 124,000,000 |