Both sine and cosine waves are periodic functions that represent oscillatory behavior. While they share many similarities, there are specific differences in how frequency, period, and wavelength are defined for each wave.
Frequency:
- Sine Wave: The frequency of a sine wave represents the number of cycles (complete oscillations) the wave completes in one second. It is typically measured in Hertz (Hz) and represents the rate at which the wave repeats.
- Cosine Wave: The frequency of a cosine wave also denotes the number of cycles the wave completes in one second. Like the sine wave, it is measured in Hertz (Hz).
Period:
- Sine Wave: The period of a sine wave is the time it takes for the wave to complete one full cycle. It is the reciprocal of the frequency and is denoted by the symbol 'T'. Mathematically, it is the time it takes for the sine function to return to the same value. The period is typically measured in seconds.
- Cosine Wave: The period of a cosine wave is also the time it takes for the wave to complete one full cycle. Like the sine wave, it is the reciprocal of the frequency and denoted by the symbol 'T'. The period is measured in seconds.
Wavelength:
- Sine Wave: The wavelength of a sine wave represents the distance between two consecutive points on the wave that are in phase. It is usually denoted by the symbol 'λ' (lambda) and is commonly measured in meters or other distance units.
- Cosine Wave: The wavelength of a cosine wave also represents the distance between two consecutive points on the wave that are in phase. Like the sine wave, it is denoted by the symbol 'λ' (lambda) and measured in meters or other distance units.
In summary, both the frequency and period of a sine wave and a cosine wave describe the rate or time it takes to complete one cycle. The wavelength, on the other hand, refers to the spatial distance between two consecutive points that exhibit the same phase. The mathematical expressions for sine and cosine waves differ only in phase, with a cosine wave being a phase-shifted version of a sine wave.