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Difficulty: MediumOscilloscopes

An oscilloscope is used to measure an alternating signal. The horizontal sweep rate (Time/Div) is set to 8 μs/div8\text{ }\mu\text{s/div}, and one complete cycle of the waveform spans exactly 5 horizontal divisions5\text{ horizontal divisions} across the graticule. What is the frequency of this signal in kilohertz (kHz\text{kHz})?

Answer: 25 kHz

Answer

The frequency of the signal is 25 kHz25\text{ kHz}.
One full waveform cycle occupies 55 horizontal divisions at 8 μs/division8\text{ }\mu\text{s/division}, giving a period of T=40 μsT = 40\text{ }\mu\text{s} (40×10−6 s40 \times 10^{-6}\text{ s}). The frequency is the reciprocal of the period (f=1T=140×10−6 s=25000 Hzf = \frac{1}{T} = \frac{1}{40 \times 10^{-6}\text{ s}} = 25{}000\text{ Hz}), which equals 25 kHz25\text{ kHz}.

Step-by-Step Solution

1
Multiply the number of horizontal graticule divisions per cycle by the time base setting to find the period (TT).
T=5 divisions×8 μs/div=40 μs=40×10−6 sT = 5\text{ divisions} \times 8\text{ }\mu\text{s/div} = 40\text{ }\mu\text{s} = 40 \times 10^{-6}\text{ s}
Horizontal divisions represent the time dimension on an oscilloscope display.
2
Calculate the frequency (ff) in hertz using the reciprocal relationship f=1Tf = \frac{1}{T}.
f=140×10−6 s=25000 Hzf = \frac{1}{40 \times 10^{-6}\text{ s}} = 25{}000\text{ Hz}
Frequency is defined as the number of cycles per second.
3
Convert the resulting frequency from hertz (Hz\text{Hz}) to kilohertz (kHz\text{kHz}).
25000 Hz1000=25 kHz\frac{25{}000\text{ Hz}}{1{}000} = 25\text{ kHz}
The question specifies the final answer unit as kilohertz.

Key Concept

Calculating waveform period and frequency from oscilloscope horizontal Time/Div settings and graticule division counts
Estimated Time:1m 0s
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Topics

Oscilloscopes

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