Question
how are wavelength and frequency related
Answers
GPT-4o mini
Wavelength and frequency are related through the speed of light in a vacuum (or in a specific medium). The relationship can be expressed with the formula:
\[ c = \lambda \cdot f \]
where:
- \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) meters per second in a vacuum),
- \( \lambda \) (lambda) is the wavelength (the distance between successive crests of a wave, typically measured in meters),
- \( f \) is the frequency (the number of wave cycles that pass a point per second, measured in hertz, or Hz).
From this equation, we can see that:
1. **Inversely Proportional Relationship**: Wavelength and frequency are inversely related. When the wavelength increases, the frequency decreases, and vice versa. This means that longer wavelengths correspond to lower frequencies, while shorter wavelengths correspond to higher frequencies.
2. **Calculating One from the Other**: You can rearrange the equation to solve for either wavelength or frequency:
- To find wavelength: \( \lambda = \frac{c}{f} \)
- To find frequency: \( f = \frac{c}{\lambda} \)
In summary, as the wavelength of a wave increases, its frequency decreases, and vice versa, while their product remains constant at the speed of light when in a vacuum.
\[ c = \lambda \cdot f \]
where:
- \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) meters per second in a vacuum),
- \( \lambda \) (lambda) is the wavelength (the distance between successive crests of a wave, typically measured in meters),
- \( f \) is the frequency (the number of wave cycles that pass a point per second, measured in hertz, or Hz).
From this equation, we can see that:
1. **Inversely Proportional Relationship**: Wavelength and frequency are inversely related. When the wavelength increases, the frequency decreases, and vice versa. This means that longer wavelengths correspond to lower frequencies, while shorter wavelengths correspond to higher frequencies.
2. **Calculating One from the Other**: You can rearrange the equation to solve for either wavelength or frequency:
- To find wavelength: \( \lambda = \frac{c}{f} \)
- To find frequency: \( f = \frac{c}{\lambda} \)
In summary, as the wavelength of a wave increases, its frequency decreases, and vice versa, while their product remains constant at the speed of light when in a vacuum.