If you double the frequency of a sinusoidal wave, the wavelength and period of the wave will change. Let's consider the relationship between frequency (f), wavelength (λ), and speed of the wave (v).
The speed of a wave is given by the equation:
v = f * λ
If we double the frequency (2f), we can rearrange the equation to solve for the new wavelength:
v = (2f) * λ'
Since the speed of the wave remains constant, the wavelength (λ') must halve to maintain the equation. Therefore, doubling the frequency results in halving the wavelength.
In terms of amplitude, doubling the frequency does not have any direct effect on the amplitude of the wave. The amplitude represents the maximum displacement of the wave from its equilibrium position and is not directly related to frequency.
The period (T) of a wave is the time it takes for one complete cycle of the wave. It is the reciprocal of frequency (T = 1/f). So, if you double the frequency, the period will be halved.
Now, let's consider what happens when you triple the frequency (3f):
v = (3f) * λ''
Again, since the speed of the wave remains constant, the wavelength (λ'') must decrease to maintain the equation. Therefore, tripling the frequency results in one-third of the original wavelength.
Similarly, the period (T'') will be one-third of the original period, as it is the reciprocal of frequency.
To summarize:
- Doubling the frequency results in halving the wavelength and halving the period.
- Tripling the frequency results in one-third of the original wavelength and one-third of the original period.
- The amplitude is not directly affected by changes in frequency.