The amplitude and frequency of a transverse wave are two distinct properties that are related but not dependent on each other.
The amplitude of a wave refers to the maximum displacement or distance that a particle in the medium (such as a string or a surface of water) moves from its equilibrium position when the wave passes through it. In simple terms, it measures the magnitude or intensity of the wave. For example, in the case of a water wave, the amplitude represents the maximum height of the wave crest or depth of the wave trough.
On the other hand, the frequency of a wave refers to the number of complete oscillations or cycles that the wave undergoes per unit of time. It is measured in hertz (Hz), which represents the number of cycles per second. In essence, it quantifies how often the wave repeats itself.
The relationship between the amplitude and frequency can be understood as follows:
Higher amplitude: If the amplitude of a transverse wave increases, it means that the particles in the medium are moving with larger displacements. This can result in a more pronounced wave with larger peaks and deeper troughs. However, the increase in amplitude does not affect the frequency of the wave. The wave can still have the same number of complete oscillations per unit of time, regardless of its amplitude.
Higher frequency: If the frequency of a transverse wave increases, it means that the wave completes more oscillations in a given time period. This results in a shorter wavelength, as the distance between successive wave crests or troughs decreases. However, the increase in frequency does not affect the amplitude of the wave. The wave can still have the same magnitude of displacement at its peaks and troughs, regardless of its frequency.
In summary, the amplitude and frequency of a transverse wave are independent properties. Changing the amplitude does not affect the frequency, and changing the frequency does not affect the amplitude. They represent different aspects of the wave's behavior and can vary independently of each other.