The relationship between wavelength (λ), frequency (f), and wave speed (v) is fundamental in the study of waves. The formula you provided, \( v = f \cdot \lambda \), illustrates this relationship:
- Wave speed (v) is the speed at which the wave propagates through a medium.
- Frequency (f) is the number of cycles (or waves) that pass a point in a unit of time, usually measured in hertz (Hz).
- Wavelength (λ) is the distance between successive crests (or troughs) of a wave, typically measured in meters.
From the equation \( v = f \cdot \lambda \), we can see that:
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Direct Relationship: If the frequency increases (more cycles per second), and the wave speed remains constant, then the wavelength must decrease (the waves are packed closer together). Conversely, if the frequency decreases, the wavelength increases.
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Constant Speed: In a given medium, the wave speed is usually constant for a particular type of wave. For example, sound waves travel at a specific speed in air at a given temperature.
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Units: The units of frequency (Hz) and wavelength (meters) combine to give wave speed in meters per second (m/s).
To summarize, the key relationship is that the product of frequency and wavelength gives the wave speed, and variations in frequency and wavelength inversely affect each other while keeping the wave speed constant in a homogeneous medium.
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