Question

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.

Answer 1

• 2.17 kHz
• 1.96 ms

Step-by-step explanation:

You want to know the frequency in kHz of a sine wave with a period of 460 μs, and its period if the frequency is reduced by a factor of 4.25.

Units

When you are interested in the frequency in kHz, it is convenient to use milliseconds (ms) to express the period. Milliseconds and kilohertz are inverse units.

The period of the given sine wave can be expressed in milliseconds as ...

460 μs = 460×(0.001 ms) = 0.460 ms

Frequency

The frequency of the wave is 1/(0.460 ms) ≈ 2.17 kHz.

Period

Because period and frequency are reciprocals of each other, reducing the frequency by a factor of 4.25 increases the period by the same factor.

The new period is 4.25×0.460 ms = 1.96 ms.

<95141404393>

Answer 2

See below

Step-by-step explanation:

Frequency = 1 / period

= 1 / 460 X 10^-6

2173.91 Hz = ~ 2.17 Khz

2.17391 kHz / 4.25 = .511 kHz <====new frequency

period = 1/frequency

= 1955 microseconds =1.96 ms