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Difficulty: MediumMeasurement of Time

A ticker-tape timer connected to a power supply operates at a frequency of 50 Hz50\text{ Hz}. A continuous strip of paper tape pulled through the timer records a sequence of dots. Calculate the total time interval, in seconds, between the 1st1\text{st} dot and the 21st21\text{st} dot on the tape.

Answer: 0.4 s

Answer

0.4 s
On a ticker tape, the time interval between consecutive dots represents one period T=1f=150 Hz=0.02 sT = \frac{1}{f} = \frac{1}{50\text{ Hz}} = 0.02\text{ s}. The total elapsed time for NN dots corresponds to (N−1)(N - 1) spaces. For 21 dots, there are 20 spaces, giving a total time of 20×0.02 s=0.40 s20 \times 0.02\text{ s} = 0.40\text{ s}.

Step-by-Step Solution

1
Find the number of spaces between dots
20 spaces
Between NN dots on a ticker-tape, there are (N−1)(N - 1) time intervals.
2
Calculate the period per space
0.02 s
The period TT is the reciprocal of the operating frequency f=50 Hzf = 50\text{ Hz}.
3
Multiply the number of spaces by the period per space
0.4 s
Total time duration is the product of the total number of intervals and the time for one interval.

Key Concept

Calculation of time interval using ticker-tape timer frequency and dot count
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Topics

Measurement of Time

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