A radio technician is testing the output of an RF signal generator using an oscilloscope. … — Armed Services Vocational Aptitude Battery (ASVAB)

A radio technician is testing the output of an RF signal generator using an oscilloscope. The horizontal timebase control is set to $250\text{ }\mu\text{s/div}$ . On the screen graticule, a continuous sinusoidal waveform is observed where exactly $2.5\text{ complete cycles}$ span across $8\text{ horizontal divisions}$ . What is the frequency of this signal, in hertz ( $\text{Hz}$ )?

Answer: 1250 Hz

Answer

1250 Hz

The total duration of the

8\text{ horizontal divisions}

250\text{ }\mu\text{s/div}

2000\text{ }\mu\text{s}

(

2\text{ ms}

). Dividing by the

2.5\text{ complete cycles}

gives a period of

T = 800\text{ }\mu\text{s} = 0.0008\text{ s}

per cycle. Taking the reciprocal gives the frequency:

f = 1 / 0.0008\text{ s} = 1250\text{ Hz}

Step-by-Step Solution

Calculate the total elapsed time across the observed graticule divisions.

Total time

= 8\text{ div} \times 250\text{ }\mu\text{s/div} = 2000\text{ }\mu\text{s}

The horizontal axis represents time, and the timebase setting indicates the duration per division.

Calculate the period (

T

) of a single cycle.

T = \frac{2000\text{ }\mu\text{s}}{2.5\text{ cycles}} = 800\text{ }\mu\text{s} = 800 \times 10^{-6}\text{ s} = 0.0008\text{ s}

The period is the time required to complete one single cycle.

Calculate the frequency (

f

) from the period.

f = \frac{1}{T} = \frac{1}{0.0008\text{ s}} = 1250\text{ Hz}

Frequency in hertz is the reciprocal of the period in seconds (

f = 1/T

Key Concept

Calculating waveform period and frequency from oscilloscope horizontal timebase settings and graticule divisions.

Estimated Time:1m 30s

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