A sinewave has a period (duration of one cycle) of 460 μs. What is the corresponding frequency of this sinewave in kHz, expressed to three significant figures (see Study Note 7.1 in the Using numbers (maths) booklet)?

If the frequency of the sinewave is now reduced by a factor of 4.25, what will be the new period value? Express your answer in ms to three significant figures.

Note: in the second part of this question, to avoid rounding errors in your calculations, use the full frequency value from the first part, not the rounded value to three significant figures.

Frequency of the sine wave = 2.17 kHz

(New) time period = 1.96 x 10^-6 ms

Frequency is defined as the number of cycles of a wave passing through a point per unit time.

Calculate the frequency using the equation:

Frequency = 1 / time period

Where time period is the duration of one cycle.

Substitute in the known value for time period (convert 460 microseconds into the SI unit for time, which is 460 x 10^-6 seconds).

Frequency = 1 / (460 x 10^-6)

Frequency = 2173.91... Hz

Ther answer needs to be in kHz, so convert this value for frequency from Hz to kHz by dividing the value by 1000.

Frequency = 2173.91... / 1000

Frequency = 2.17 kHz (3sf)

For the second part of the question, the frequency of the sine wave is reduced by SF 4.25, so divide the previous calculated frequency of 2173.91... Hz by 4.25.

2173.91.... / 4.25 = 511.50..... Hz

Using the same frequency equation from earlier, rearrange it to find the value of the new time period.

Frequency = 1 / time period

Time period = 1 / frequency

Substitute the known value for the reduced frequency (511.50.... Hz) into the equation.

Time period = 1 / 511.50.....

Time period = 0.001955 seconds

The answer needs to be in milliseconds, so convert the value for time period from seconds to milliseconds by dividing the value by 1000.

Time period = 0.001955 / 1000

Time period = 1.96 x 10^-6 ms