A sinewave has a period (duration of one cycle) of 535 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 sinewave frequency is now increased 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 value rounded to three significant figures.

### Part 1: Finding the frequency of the sinewave

The frequency \( f \) of a sinewave is the reciprocal of the period \( T \), which is given by the formula:

\[
f = \frac{1}{T}
\]

Here, the period \( T \) is 535 μs (microseconds). First, we need to convert this into seconds:

\[
T = 535 \times 10^{-6} \, \text{seconds}
\]

Now, we can calculate the frequency:

\[
f = \frac{1}{535 \times 10^{-6}} \, \text{Hz}
\]

\[
f \approx 1870.56 \, \text{Hz}
\]

To express this in kHz:

\[
f = \frac{1870.56}{1000} \, \text{kHz} \approx 1.871 \, \text{kHz}
\]

So, the frequency is approximately **1.871 kHz** to three significant figures.

### Part 2: Finding the new period after the frequency increase

The sinewave's frequency is now increased by a factor of 4.25. Let's first calculate the new frequency:

\[
f_{\text{new}} = 1.87056 \times 4.25 \, \text{kHz}
\]

Now we calculate the new period \( T_{\text{new}} \), remembering that the period is the reciprocal of the frequency:

\[
T_{\text{new}} = \frac{1}{f_{\text{new}}}
\]

I'll now compute the new frequency and period using the exact values for precision.

A sinewave has a period (duration of one cycle) of 535 μs. What is the corresponding frequency of this sinewave in kHz, expressed to three significant figures? If the sinewave frequency is now increased 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 value rounded to three significant figures.

Find the frequency of a sinewave with a period of 535 μs, expressed in kHz to three significant figures, and calculate the new period when the frequency is increased by a factor of 4.25. This problem involves understanding wave properties, unit conversions, and precise calculations to avoid rounding errors. Suitable for students in Grades 10-12.

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