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# Fundamental Properties Help

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## Introduction

All waves, no matter what the medium or mode, have three different but interdependent properties. The wavelength is the distance between identical points on two adjacent waves. It is measured in meters. The frequency is the number of wave cycles that occur or that pass a given point per unit time. It is specified in cycles per second, or hertz. The propagation speed is the rate at which the disturbance travels through the medium. It is clocked in meters per second. These three properties are related: Speed equals wavelength times frequency . Consistent units must be used for this relation to have meaning.

## Period, Frequency, Wavelength, And Propagation Speed

Sometimes it’s easier to talk about a wave’s period rather than its frequency. The period T (in seconds) of a sine wave is the reciprocal of the frequency f (in hertz). Mathematically, the following formulas hold:

f = 1/ T = T −1

T = 1/ f = f −1

If a wave has a frequency of 1 Hz, its period is 1 s. If the frequency is one cycle per minute (1/60 Hz), the period is 60 s. If the frequency is one cycle per hour (1/3600 Hz), the period is 3,600 s, or 60 min.

The period of a wave is related to the wavelength λ (in meters) and the propagation speed c (in meters per second) as follows: Wavelength equals speed times period . Mathematically:

λ = cT

This gives rise to other formulas:

λ = c/f

c = f λ

c = λ/ T

#### Problem

If the child whirling the object on the string slows down the speed so that the object whirls at the rate of one revolution every 2 seconds instead of one revolution per second, what happens to the wavelength of the graph in Fig. 17-1 , assuming that time is plotted on the same scale horizontally?

#### Solution

Consider the formula λ = c/f above. Cutting the frequency in half doubles the wavelength. If each horizontal division represents a constant amount of time, then if the object revolves half as fast, the wavelength becomes twice as long.

## Frequency Units

Audible acoustic waves repeat at intervals that are only a small fraction of a second. The lowest sound frequency a human being can hear is about 20 cycles per second, or 20 hertz (20 Hz). The highest frequency an acoustic wave can have and still be heard by a person with keen ears is a thousand times higher: 20,000 Hz.

Radio waves travel in a different medium than sound waves. Their lowest frequency is a few thousand hertz, and their highest frequencies range into the trillions of hertz. Infrared (IR) and visible-light waves occur at frequencies much higher than radio waves. Ultraviolet (UV) waves, x -rays, and gamma (γ) rays range into quadrillions and quintillions of hertz, vibrating more than 1 trillion times faster than middle C on the musical scale.

To denote high frequencies, scientists and engineers use frequency units of kilohertz (kHz), megahertz (MHz), gigahertz (GHz), and terahertz (THz). Each unit is a thousand times higher than the previous one in this succession. That is, 1 kHz = 1,000 Hz, 1 MHz = 1,000 kHz, 1 GHz = 1,000 MHz, and 1 THz = 1,000 GHz.

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