How does changing the wavelength of a wave while keeping its speed constant affect its frequency?
To understand how changing the wavelength of a wave while keeping its speed constant affects its frequency, we need to review the formula that relates wavelength, frequency, and speed.
The formula is:
Speed = Wavelength × Frequency
In this formula, "Speed" represents the speed at which the wave travels through a medium, "Wavelength" represents the distance between two consecutive points on the wave, and "Frequency" represents the number of complete cycles of the wave that pass through a point in one second.
Now let's consider the scenario where the speed of the wave remains constant, but the wavelength changes.
If you decrease the wavelength, the frequency of the wave will increase. This is because the speed is constant, and since Speed = Wavelength × Frequency, reducing the wavelength results in an increase in frequency in order to keep the speed constant.
Conversely, if you increase the wavelength, the frequency of the wave will decrease. Again, this is because the speed stays constant, and to maintain that speed, an increase in wavelength requires a decrease in frequency.
So, to summarize:
- If the wavelength of a wave is decreased while keeping the speed constant, the frequency of the wave increases.
- If the wavelength of a wave is increased while keeping the speed constant, the frequency of the wave decreases.
To calculate the new frequency, you can rearrange the formula:
Frequency = Speed / Wavelength
By plugging in the given values of speed and wavelength, you can determine the resulting frequency.
When changing the wavelength of a wave while keeping its speed constant, the frequency of the wave will also change. In fact, the frequency and wavelength of a wave are inversely proportional to each other. This means that as the wavelength increases, the frequency decreases, and vice versa.
The relationship between wavelength (λ), frequency (f), and speed (v) of a wave can be expressed mathematically using the equation:
v = λ * f
where v is the speed of the wave.
Since the speed is constant, any change in wavelength will result in a corresponding change in frequency to maintain this equation.
For example, if the wavelength of a wave is doubled while the speed remains constant, the frequency would halve. Similarly, if the wavelength is halved, the frequency would double.
In summary, changing the wavelength of a wave while keeping its speed constant will cause a proportional change in the frequency of the wave.