# 4.6.2 Calculating Frequency

### Calculating Frequency

• Frequency (f) is defined by the equation: • Where T is the time period, the time taken for one complete oscillation or cycle of the wave

#### Worked Example

Calculate the frequency of the following wave: Step 1: List the known quantities

• Period, T = 0.28 ms = 0.28 × 10-3 s

Step 2: Write down the frequency equation Step 3: Substitute in the values

f = 1 ÷ (0.28 × 10-3) = 3571.4 = 3.57 kHz

#### Exam Tip

When using the frequency equation, always make sure the time period is in seconds to get the value of the frequency in Hertz (Hz)

### Determining Frequency from an Oscilloscope

• A Cathode-Ray Oscilloscope (CRO) is a laboratory instrument used to display, measure and analyse waveforms of electrical circuits
• It can therefore be used as an a.c and d.c voltmeter
• An a.c voltage on an oscilloscope is represented as a transverse wave
• Therefore you can determine its frequency, time period and peak voltage
• A d.c voltage on an oscilloscope is represented as a horizontal line at the relevant voltage
• The x-axis is the time and the y-axis is the voltage (or y-gain)
• The frequency of a wave is determined from the time period of the wave
• The period can be determined from the time-base
• This is how many seconds each division represents measured commonly in s div-1 or s cm-1
• Dividing the total time by the number of wavelengths will give a value for T
• Use as many wavelengths shown on the screen as possible to reduce uncertainties
• The frequency is then determined using the equation: #### Worked Example

A cathode-ray oscilloscope (c.r.o.) is used to display the trace from a sound wave. The time-base is set at 7 µs mm-1. What is the frequency of the sound wave?

A    2.4 Hz          B     24 Hz             2.4 kHz             24 kHz

#### Exam Tip

The time-base setting varies with units for seconds (commonly ms) and the unit length (commonly mm). Unit conversions are very important when calculating the time period and frequency.

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