Velocity, period, and frequency are interconnected properties of a wave. The relationship between them depends on the type of wave being considered.
In general, the velocity of a wave (v) can be expressed as the product of its wavelength (λ) and its frequency (f):
v = λf
Here's how velocity, period, and frequency are related for different types of waves:
Transverse Waves:
- Velocity (v): In the case of transverse waves, such as electromagnetic waves, the velocity represents the speed at which the wave propagates through a medium or through space.
- Wavelength (λ): It is the distance between two consecutive peaks or troughs of the wave.
- Frequency (f): It is the number of complete oscillations (cycles) of the wave that occur per unit of time.
- Period (T): It is the time required for one complete oscillation (cycle) of the wave.
The relationship between these quantities can be expressed as follows: v = λf = λ/(1/T) = λT
In this case, as the wavelength increases, the frequency decreases, and vice versa. The period is the reciprocal of the frequency, so a high frequency corresponds to a short period, and a low frequency corresponds to a long period.
Longitudinal Waves:
- Velocity (v): In the case of longitudinal waves, such as sound waves, the velocity represents the speed at which compressions and rarefactions propagate through a medium.
- Wavelength (λ): It is the distance between two consecutive compressions or rarefactions of the wave.
- Frequency (f): It is the number of complete compressions and rarefactions that occur per unit of time.
- Period (T): It is the time required for one complete compression and rarefaction.
The relationship between these quantities is the same as for transverse waves: v = λf = λ/(1/T) = λT
Similarly, for longitudinal waves, as the wavelength increases, the frequency decreases, and vice versa. The period is the reciprocal of the frequency, so a high frequency corresponds to a short period, and a low frequency corresponds to a long period.
In summary, the velocity of a wave is equal to the product of its wavelength and frequency. For both transverse and longitudinal waves, as the wavelength increases, the frequency decreases, and vice versa. The period is the reciprocal of the frequency, so a high frequency corresponds to a short period, and a low frequency corresponds to a long period.