What is the relationship between the frequency and wavelength of a wave, if the speed remains constant but the wavelength is increased?
To understand the relationship between frequency and wavelength, let's first establish some basic concepts.
The wavelength of a wave is the distance between two corresponding points on the wave, such as the distance between two crests or two troughs. It is usually represented by the Greek letter lambda (λ) and is measured in units of length, such as meters (m).
The frequency of a wave is the number of complete cycles of the wave that pass a given point per second. It is represented by the symbol 'f' and is measured in units of hertz (Hz), which is equal to one cycle per second.
The speed of a wave is the rate at which the wave moves through space. It is represented by the symbol 'v' and is measured in units of meters per second (m/s).
Now, let's consider the situation where the speed of the wave remains constant, but the wavelength is increased.
The formula for the speed of a wave is given by:
v = f * λ
Here, 'v' represents the speed of the wave, 'f' represents the frequency, and 'λ' represents the wavelength.
If the speed remains constant (v is constant), and the wavelength (λ) increases, the only way for this equation to hold is if the frequency (f) decreases proportionally.
In other words, when the wavelength increases while the speed remains constant, the frequency decreases.
This relationship can be intuitively understood by considering that if the wavelength becomes larger, it takes more time for one complete cycle of the wave to pass a given point, resulting in a decrease in frequency.
In summary, as the wavelength of a wave increases while the speed remains constant, the frequency decreases.