Frequency (f) is defined as the number of complete wave cycles that pass a fixed point every second, measured in Hertz (Hz). A frequency of Hz means that ten full waves pass a specific location in exactly one second.
Period (T) is the time required for one complete wave cycle to pass a given point, measured in seconds (s). The relationship between these two variables is reciprocal, expressed by the formula or .
Wave speed (v) is the speed at which energy is transferred through a medium, calculated as the distance a wave travels per unit of time. It is a property of the medium itself and remains constant for a specific wave type in a uniform material.
The Wave Equation relates speed, frequency, and wavelength: . This formula demonstrates that for a constant wave speed, frequency and wavelength are inversely proportional; if the frequency increases, the wavelength must decrease to maintain the same speed.
It is vital to distinguish between the motion of the wave and the motion of the particles. In transverse waves, particles oscillate perpendicular to the direction of energy transfer, while in longitudinal waves, they oscillate parallel to it.
| Feature | Displacement-Distance Graph | Displacement-Time Graph |
|---|---|---|
| X-axis | Distance (m) | Time (s) |
| Peak-to-Peak | Wavelength () | Period () |
| Purpose | Shows wave shape in space | Shows particle history in time |
Always check the units on the axes of a wave graph before performing calculations. If the x-axis is in centimeters or milliseconds, you must convert these to meters or seconds to ensure the wave speed is calculated in .
When identifying amplitude, ensure you measure from the center line (equilibrium) to the peak. A common mistake is measuring the total vertical distance from peak to trough, which is actually twice the amplitude.
Verify the reasonableness of your answers by checking the relationship . If you calculate a very high frequency but a very long wavelength for a wave in a slow medium, you likely have a calculation error.
