Wave Equation

Fundamental wave equation showing relationship between all three quantities

Frequency Formula

Find frequency when wavelength and velocity are known

Photon Energy Formula

Where: E is energy (Joules), h is Planck's constant (6.626×10⁻³⁴ J·s), c is speed of light, f is frequency, λ is wavelength

Key Insight: Shorter wavelengths have higher energy. This is why ultraviolet light (short λ) is more energetic and potentially harmful than infrared light (long λ).

Given Information:

• Frequency (f) = 5×10¹⁴ Hz
• Speed of light (c) = 3×10⁸ m/s
• Need to find: Wavelength (λ)

Solution Steps:

Result: The wavelength is 600 nm, which corresponds to orange light in the visible spectrum. This demonstrates the inverse relationship: high frequency results in short wavelength.

What is wavelength?

Wavelength is the distance between consecutive corresponding points of the same phase on a wave, such as two adjacent peaks or troughs. It is measured in meters (m) or subunits like nanometers (nm) for light. The wavelength formula is λ = v/f, where λ is wavelength, v is wave velocity, and f is frequency. Wavelength determines many wave properties including color for visible light.

How do you calculate wavelength?

To calculate wavelength, use the formula λ = v/f where v is wave velocity and f is frequency. For light waves, use λ = c/f where c is the speed of light (3×10⁸ m/s). For example, light with frequency 5×10¹⁴ Hz has wavelength λ = (3×10⁸)/(5×10¹⁴) = 6×10⁻⁷ m = 600 nm. Always ensure units are consistent: velocity in m/s and frequency in Hz gives wavelength in meters.

What is the formula for wavelength?

The wavelength formula is λ = v/f, where λ (lambda) is wavelength in meters, v is wave velocity in m/s, and f is frequency in Hz. For electromagnetic waves, this becomes λ = c/f where c = 3×10⁸ m/s is the speed of light. The relationship can also be expressed as v = λf, showing that wavelength and frequency are inversely proportional when wave speed is constant.

What is the relationship between wavelength and frequency?

Wavelength and frequency have an inverse relationship: as wavelength increases, frequency decreases, and vice versa. This relationship is expressed by the equation v = λf where v is constant wave velocity. For light in vacuum, c = λf where c is the speed of light. Mathematically, λ = c/f shows that doubling frequency halves wavelength. High frequency waves (like X-rays) have short wavelengths, while low frequency waves (like radio) have long wavelengths.

How do you find frequency from wavelength?

To find frequency from wavelength, rearrange the wavelength formula to f = v/λ where f is frequency, v is wave velocity, and λ is wavelength. For light waves, use f = c/λ where c = 3×10⁸ m/s. For example, light with wavelength 500 nm (5×10⁻⁷ m) has frequency f = (3×10⁸)/(5×10⁻⁷) = 6×10¹⁴ Hz. Convert wavelength to meters first for correct calculation.

What is the wavelength of visible light?

Visible light wavelengths range from approximately 380 nm (violet) to 700 nm (red). Specific colors have characteristic wavelengths: violet (380-450 nm), blue (450-495 nm), green (495-570 nm), yellow (570-590 nm), orange (590-620 nm), and red (620-700 nm). The human eye is most sensitive to green light around 555 nm. Wavelengths outside this range (UV < 380 nm, IR > 700 nm) are invisible to humans.

How does wavelength affect energy?

For electromagnetic radiation, wavelength and energy have an inverse relationship expressed by E = hc/λ, where E is energy, h is Planck's constant (6.626×10⁻³⁴ J·s), c is the speed of light, and λ is wavelength. Shorter wavelengths carry more energy: gamma rays (very short λ) are extremely energetic, while radio waves (very long λ) have low energy. This is why UV light can cause sunburn while radio waves cannot.