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Use the relationship between frequency and period.
When the frequency becomes two times smaller, the period gets two times greater.
Formula | Substitution | Decimal Form | |
---|---|---|---|
Intercepts | (0,0), (1/2*2Ď€/b,0), (2Ď€/b,0) | (0,0), (1/2*2Ď€/2000Ď€,0), (2Ď€/2000Ď€,0) | (0,0), (0.0005,0), (0.001,0) |
Maximum | (1/4* 2Ď€/b, a) | (1/4* 2Ď€/2000Ď€, 2 ) | (0.00025,2) |
Minimum | (3/4*2Ď€/b, - a ) | (3/4*2Ď€/2000Ď€, - 2) | (0.00075,- 2) |
We can graph the function by plotting calculated points and connecting them with a smooth curve. Let's do it!
We draw a graph of a function of maximum pressure P produced by pure tone with a frequency of 1000 hertz. Finally, we can compare it with the original function P = 2 sin 2000Ď€t to see how the graph of a function changed, when we changed a frequency.
We changed the frequency from 2000 hertz into 1000 hertz, which means that it became two times smaller. As a result, we can see that the period of a graph became two times greater. In other words the graph is horizontally stretched two times. This does not surprise us, let's again look at the relationship involving frequency and period. frequency=1/period Their inverse proportionality implies that when the frequency gets two times smaller, then the period gets two times greater. This is the same conclusion as we observed at the graph.