Cathode-Ray Oscilloscope (Cambridge International A-Level Physics)

Spec point — 7.1.3

Cathode-ray oscilloscope

• A cathode-ray oscilloscope is a laboratory instrument used to display, measure and analyse waveforms of electrical circuits

• An a.c. current on an oscilloscope is represented as a transverse wave

  • The oscilloscope can be used to determine its frequency and amplitude

• 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)

Cathode-ray oscilloscope display

Diagram of cathode-ray oscilloscope display showing wavelength and time-base setting

• The period of the wave can be determined from the time-base

  • Time-base is how many seconds each division represents measured commonly in s div-1****or s cm^-1

• Count the number of wavelengths shown on the screen

• Divide the total time by the number of wavelengths to obtain the time period T

• Calculate the frequency of the wave using $f=\frac{1}{T}$

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

C. 2.4 kHz

D. 24 kHz

Answer: C

Step 1: Determine the period of the wave:

• One full wave covers three horizontal squares, which is a distance of 6 cm

• There are 60 mm in 6 cm

  • Each mm represents a time of 7 μs
  • Time period, T = 60 × (7 × 10⁻⁶) = 4.2 × 10⁻⁴ s

Step 2: Use the frequency equation to determine frequency:

• Recall the frequency equation

$f=\frac{1}{T}=\frac{1}{4.2\times10^{-4}}=2380\mathrm{Hz}$

• Recall that 1000 Hz = 1 kHz and the answer must be given to 2 significant figures

$f=2.4\mathrm{kHz}$

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