   Chapter 6, Problem 4PS

Chapter
Section
Textbook Problem

Suppose you are standing 225 m from a radio transmitter. What is your distance from the transmitter in terms of the number of wavelengths if (a) the station is broadcasting at 1150 kHz (on the AM radio band)? (1kHz = 1 × 103 Hz) (b) the station is broadcasting at 98.1 MHz (on the FM radio band)? (1 MHz × 106 Hz)

(a)

Interpretation Introduction

Interpretation:

The distance in terms of number of wavelength from the radio transmitter has to be calculated if the station is broadcasting at 1150kHz.

Concept introduction:

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

• The units Hz=s1
• Thenumberofwavelengths=distancewavelength
Explanation

The number of wavelengths is calculated.

Given,

The frequency of radio wave is 1150kHz=1150×103Hz

The speed of light is 2.998×108m/s

The units Hz=s1

The wavelength of the radio wave is calculated by using the equation,

λ=cν=2

(b)

Interpretation Introduction

Interpretation:

The distance in terms of number of wavelength from the radio transmitter has to be calculated if the station is broadcasting at 98.1MHz.

Concept introduction:

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

• The units Hz=s1
• Thenumberofwavelengths=distancewavelength

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