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Chapter 15: Problem 12

What is the period of the hand on a clock that measures the minutes? What is its frequency?

Short Answer

Expert verified
The period is 60 minutes (3600 seconds), and the frequency is \(\frac{1}{3600}\) Hz.

Step by step solution

01

- Understand the Definition of Period

The period of a clock hand is the amount of time it takes to complete one full revolution. For the minute hand on a clock, this means moving from the 12 back to the 12.
02

- Determine the Period of the Minute Hand

The minute hand makes one full revolution every 60 minutes. Hence, the period of the minute hand is 60 minutes. To convert this into seconds, multiply by 60: \[ 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3600 \text{ seconds} \]
03

- Understand the Definition of Frequency

Frequency is the number of cycles (or revolutions) per unit time. It is the reciprocal of the period.
04

- Calculate the Frequency of the Minute Hand

The period in seconds is 3600 seconds per cycle. The frequency is given by: \[ \text{Frequency} = \frac{1}{\text{Period}} = \frac{1}{3600 \text{ seconds}} = \frac{1}{3600} \text{ Hz} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Period of Motion
The period of motion is the time it takes for an object to complete one full cycle of movement. In the context of a clock, the period for the minute hand is the time it takes to move from the 12, all the way around the clock face, and back to the 12 again.
This is known as a complete revolution.
For a standard clock, the minute hand completes one revolution every 60 minutes.
Understanding the period is vital in various areas of physics and engineering since it helps describe how long a repeated action takes to repeat itself completely.
Frequency Calculation
Frequency measures how often something occurs in a specific period of time.
It is calculated as the number of cycles per unit time and is the reciprocal of the period.
For the clock's minute hand, since the period is 60 minutes (or 3600 seconds), the frequency can be calculated using the formula:

$$ \text{Frequency} = \frac{1}{\text{Period}} $$

Applying this formula gives:
$$ \text{Frequency} = \frac{1}{3600 \text{ seconds}} = \frac{1}{3600} \text{ Hz} $$
Frequency is measured in Hertz (Hz), where 1 Hz is equal to one cycle per second.
In this example, the minute hand's frequency is $$ \frac{1}{3600} \text{ Hz} $$ indicating it completes one cycle every 3600 seconds.
Time Conversion
Converting time units is an essential skill in solving many physics and engineering problems.
To find the period of the minute hand in seconds, we need to convert minutes to seconds.
Since there are 60 seconds in a minute, we can write the period in different units.
For example, the minute hand's period is 60 minutes, converting this to seconds involves multiplying by 60:

$$ 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3600 \text{ seconds} $$
Converting time may also involve other units like hours, days, or milliseconds, but the principles remain the same.
Understanding how to convert between units ensures we can break down complex problems and solve them step by step.

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Most popular questions from this chapter

A periodic wave on a string has a wavelength of \(25 \mathrm{cm}\) and a frequency of \(3 \mathrm{Hz}\). What is the speed of the wave?

If a mass on a spring has a frequency of \(4 \mathrm{Hz}\), what is its period?

Two point sources produce waves of the same wavelength and are in phase. At a point midway between the sources, would you expect to find a node or an antinode? Explain.

A mass is oscillating up and down on a vertical spring. If the mass is increased, will the period of oscillation increase, decrease, or stay the same? Will the frequency increase, decrease, or stay the same? Explain.

Two waves have the same speed but one has twice the frequency. Which wave has the longer wavelength? Explain.
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