Wave Motion - Mission WM2 Detailed Help

Which of the following two quantities are reciprocals of each other?


 
Here is a short little activity your can do on your own. Clench your fingers together and rap on the table one time per second. How much time elapses between each rap on the table? Now rap on the table two times per second. How much time elapses between each rap. Finally (if you can do it), rap on the table three times per second. How much time elapses between each rap.

You hopefully noticed the following pattern:
1 rap/second ---> 1 second between raps
2 raps/second ---> 1/2 seconds between raps
3 raps/second ---> 1/3 seconds between raps

For any periodic and repeating event, there are two quantities that describe the event that are reciprocals of each other. The number of occurrences per second and the time elapsed between occurrences are reciprocals of each other.


 
A wave is a periodic and repeating event that reoccurs in a regular time pattern. Particles of the medium vibrate back-and-forth in a regular time pattern. The frequency of the wave describes how often they vibrate - the number of vibrations per second. And the period of the wave describes the time elapsed between vibrations - the time required for a particle of the medium to complete its vibration. These two quantities are reciprocals of each other.


 
The reciprocal nature of frequency (f) and period (T) are seen in the following mathematical definitions.
 
f = # of cycles / time           T = amount of time / cycle


 

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