Which of the following are related to one another, and which is independent of the others?
(Amplitude, Frequency, Period, Wavelength). Please detail help and answer..
To determine which of the given terms are related to each other and which one is independent, let's first understand what each term represents:
1. Amplitude: It refers to the maximum displacement or height of a wave from its rest position. In simple terms, it measures the intensity or strength of a wave.
2. Frequency: It represents the number of complete cycles or oscillations of a wave that occur in one second. It is usually measured in Hertz (Hz).
3. Period: It is the time taken for one complete cycle or oscillation of a wave to occur. It is the inverse of frequency, meaning that the period is the reciprocal of the frequency.
4. Wavelength: It is the distance between two consecutive corresponding points of a wave, such as two crests or two troughs. It is usually represented by the Greek letter lambda (λ) and is measured in units such as meters (m) or nanometers (nm).
Now, let's analyze the relationship between these terms:
- Amplitude and Frequency: They are independent of each other. The amplitude of a wave does not affect its frequency, and vice versa. For example, increasing the amplitude of a sound wave does not change its pitch (frequency).
- Frequency and Period: They are inversely related. The period is the reciprocal of the frequency, which means that as the frequency increases, the period decreases, and vice versa. Mathematically, Period = 1 / Frequency.
- Frequency and Wavelength: They are directly related. The frequency of a wave and its wavelength are proportional to each other. In other words, as the frequency of a wave increases, the wavelength decreases, and vice versa. Mathematically, the relationship is represented as: Speed of Wave = Frequency × Wavelength.
Therefore, the terms Amplitude and Wavelength are independent of the others, while Frequency and Period are inversely related, and Frequency and Wavelength are directly related.