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In the context of wave functions, how does increasing the frequency of a wave affect its wavelength , assuming the wave speed remains constant?
A
The wavelength first increases, then decreases as frequency increases.
B
The wavelength increases as frequency increases.
C
The wavelength remains unchanged as frequency increases.
D
The wavelength decreases as frequency increases.
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1
Recall the fundamental relationship between wave speed (v), frequency (f), and wavelength (\(\lambda\)), which is given by the equation:
\[v = f \times \lambda\]
Since the wave speed \(v\) is constant, we can rearrange the equation to express wavelength in terms of frequency:
\[\lambda = \frac{v}{f}\]
Analyze how wavelength \(\lambda\) changes when frequency \(f\) increases: because \(v\) is constant, increasing \(f\) means the denominator of the fraction increases.
As the denominator increases, the overall value of \(\lambda = \frac{v}{f}\) decreases, indicating an inverse relationship between wavelength and frequency.
Therefore, when frequency increases while wave speed remains constant, the wavelength decreases.