An audio technician connects an oscilloscope to analyze a recurring tone from a signal gen… — Armed Services Vocational Aptitude Battery (ASVAB)

An audio technician connects an oscilloscope to analyze a recurring tone from a signal generator. The horizontal Time/Div control is set to $250\text{ }\mu\text{s/div}$ . On the graticule display, exactly two complete cycles of the sine wave span $8\text{ horizontal divisions}$ . What is the frequency of the audio signal?

A
$500\text{ Hz}$
$1\text{ kHz}$ Answer
C
$4\text{ kHz}$
D
$100\text{ Hz}$

Answer

The frequency of the audio signal is

1\text{ kHz}

(

1{}000\text{ Hz}

One complete sine wave cycle occupies

\frac{8\text{ divisions}}{2} = 4\text{ divisions}

. Multiplying by the horizontal timebase of

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

gives a period of

T = 1{}000\text{ }\mu\text{s} = 1\text{ ms} = 0.001\text{ s}

. The frequency is

f = \frac{1}{T} = \frac{1}{0.001\text{ s}} = 1{}000\text{ Hz} = 1\text{ kHz}

Step-by-Step Solution

Determine the number of horizontal divisions occupied by one complete cycle.

\text{Divisions per cycle} = \frac{8\text{ divisions}}{2\text{ cycles}} = 4\text{ div/cycle}

The period of a periodic wave is defined by the horizontal duration of one full cycle.

Calculate the period (

T

) of the waveform by multiplying divisions per cycle by the horizontal timebase scale.

T = 4\text{ div} \times 250\text{ }\mu\text{s/div} = 1000\text{ }\mu\text{s} = 1 \times 10^{-3}\text{ s}

The Time/Div control establishes the time value represented by each graticule division.

Calculate the frequency (

f

) using the reciprocal formula

f = \frac{1}{T}

f = \frac{1}{1 \times 10^{-3}\text{ s}} = 1000\text{ Hz} = 1\text{ kHz}

Frequency is the inverse of the period in seconds.

Key Concept

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

Estimated Time:1m 0s

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