Question

A digital frequency meter counts 5000 pulses during a gate time of 0.1 s. The measured frequency is

• A. 500 Hz
• B. 5 kHz
• C. 50 kHz
• D. 500 kHz

Hint:

Frequency means counts per one full second. If the meter registers 5000 counts in just one-tenth of a second (0.1 s), it will register ten times as many counts in a full second: \(5000 \times 10 = 50,000\text{ Hz} = 50\text{ kHz}\).

Answer 1

The Correct Option is C

Concept: A digital frequency meter operates by counting the number of incoming signal pulses (\(N\)) that occur within a strictly controlled period known as the gate time (\(t_g\)). Since frequency (\(f\)) represents the number of cycles or pulses that occur per unit second, it is calculated as: \[ f = \frac{\text{Number of counted pulses } (N)}{\text{Gate time opening period } (t_g)} \]

Step 1: Substitute the given values into the frequency formula. The system parameters provided are:
• Total pulses counted (\(N\)) = 5000 pulses
• Gate time period interval (\(t_g\)) = 0.1 seconds Applying the formula: \[ f = \frac{5000}{0.1\text{ s}} = 5000 \times 10 = 50000\text{ Hz} \]

Step 2: Convert the frequency unit into kilohertz (kHz). To convert from Hz to kHz, divide the result by 1000: \[ f = \frac{50000}{1000}\text{ kHz} = 50\text{ kHz} \] Hence, the measured frequency of the input signal is 50 kHz, matching option (C).