In a sine wave, amplitude, frequency, and wavelength are interconnected properties that describe different aspects of the wave.
Amplitude: The amplitude of a sine wave refers to the maximum displacement or distance from the equilibrium position of the wave. It represents the strength or intensity of the wave and is typically measured as the distance from the baseline (equilibrium) to the peak (crest) of the wave. Amplitude determines the wave's maximum displacement from its resting position.
Frequency: Frequency is the number of complete cycles or oscillations of a wave that occur per unit of time. It is measured in hertz (Hz) and represents how many times the wave repeats itself within a given time frame. In the case of a sine wave, one complete cycle consists of a crest followed by a trough and returning to the starting point. The frequency determines the pitch of a sound wave or the rate of oscillation of a periodic wave.
Wavelength: Wavelength refers to the spatial length of one complete cycle of a wave. It is measured as the distance between two corresponding points in the wave, such as between two adjacent crests or troughs. In the case of a sine wave, the wavelength is the distance between two consecutive points where the wave completes one full cycle. Wavelength is typically represented by the Greek letter lambda (λ) and is inversely proportional to the frequency of the wave.
The relationship between these properties can be summarized as follows:
Higher amplitude: A higher amplitude means the wave extends further from the equilibrium position, resulting in a larger peak and trough. Increasing the amplitude does not affect the frequency or wavelength of the wave.
Higher frequency: A higher frequency means the wave oscillates more frequently within a given time frame. Increasing the frequency of a sine wave reduces its wavelength while keeping the amplitude constant. As the frequency increases, the wave cycles become more compressed, resulting in shorter wavelengths.
Longer wavelength: A longer wavelength corresponds to a lower frequency. Increasing the wavelength of a sine wave while keeping the amplitude constant results in a decrease in frequency. The wave cycles become more spread out, and the time between successive cycles increases.
In summary, amplitude determines the strength or intensity of the wave, frequency determines the rate of oscillation or pitch, and wavelength determines the spatial length of one complete cycle. They are interconnected properties of a sine wave, with frequency and wavelength being inversely related.