Physics, 23.07.2019 00:30 croxy0514

Am radio signals have frequencies between 550 khz and 1600 khz (kilohertz) and travel with a speed of 3.00 ✕ 108 m/s. what are the wavelengths of these signals? 550 khz signal m 1600 khz signal m on fm, the frequencies range from 88.0 mhz to 108 mhz (megahertz) and travel at the same speed. what are their wavelengths? 88.0 mhz signal m 108 mhz signal m

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1) am radio waves

The lowest and highest frequencies of the radio signals are:
$f_L = 550 kHz = 5.5 \cdot 10^5 Hz$
$f_H = 1600 kHz = 1.6 \cdot 10^6 Hz$

The speed of the waves is the speed of light, $c=3 \cdot 10^8 m/s$ , so to find the corresponding wavelengths we can use the basic relationship between frequency, wavelength and speed of a wave:
$\lambda = \frac{c}{f}$
where f is the frequency and $\lambda$ the wavelength.

The wavelength corresponding to the lowest frequency is:
$\lambda_L= \frac{c}{f_L}= \frac{3 \cdot 10^8 m/s}{5.5 \cdot 10^5 Hz}=545 m$
while the wavelength corresponding to the highest frequency is
$\lambda_H = \frac{c}{f_H}= \frac{3\cdot 10^8 m/s}{1.6 \cdot 10^6 Hz}=187.5 m$

So, the range of wavelengths is [187.5-545] m.

2) fm radio waves
This time, the lowest and highest frequencies of the radio waves are:
$f_L=88.0 MHz = 8.8 \cdot 10^7 Hz$
$f_H=108 MHz=1.08 \cdot 10^8 Hz$

So the corresponding wavelengths are:
$\lambda_L= \frac{c}{f_L}= \frac{3 \cdot 10^8 m/s}{8.8 \cdot 10^7 Hz}=3.4 m$
$\lambda_H = \frac{c}{f_H}= \frac{3 \cdot 10^8 m/s}{1.08 \cdot 10^8 m/s}=2.8 m$

Therefore, the range of wavelengths of the rm radio signals is [2.8-3.4] m.

Answer from: williamschris462

The wavelength of these signals are :

AM Radio Signals → 188 m < λ < 545 m

FM Radio Signals → 2.78 m < λ < 3.41 m

$\texttt{ }$

Further explanation

Let's recall the speed of wave formula as follows:

$\boxed {v = \lambda \times f}$

where:

v = speed of wave ( m/s )

λ = wavelength ( m )

f = frequency of wave ( Hz )

Let us now tackle the problem!

$\texttt{ }$

Given:

maximum frequency of AM radio signals = f_max = 1600 kHz

minimum frequency of AM radio signals = f_min = 550 kHz

maximum frequency of FM radio signals = f_max = 108 MHz

minimum frequency of FM radio signals = f_min = 88.0 MHz

speed of wave = v = 3.00 × 10⁸ m/s

Asked:

wavelength = λ = ?

Solution:

Part A:

AM Radio Signals

$550 \texttt{ kHz} < f < 1600 \texttt{ kHz}$

$550 \texttt{ kHz} < \frac{v}{\lambda} < 1600 \texttt{ kHz}$

$550 \texttt{ kHz} < \frac{3.00 \times 10^8}{\lambda} < 1600 \texttt{ kHz}$

$\frac{3.00 \times 10^8}{1600 \times 10^3} \texttt{ m} < \lambda < \frac{3.00 \times 10^8}{550 \times 10^3} \texttt{ m}$

$\boxed {188 \texttt{ m} < \lambda < 545 \texttt{ m}}$

$\texttt{ }$

Part B:

FM Radio Signals

$88.0 \texttt{ MHz} < f < 108 \texttt{ MHz}$

$88.0 \texttt{ MHz} < \frac{v}{\lambda} < 108 \texttt{ MHz}$

$88.0 \texttt{ MHz} < \frac{3.00 \times 10^8}{\lambda} < 108 \texttt{ MHz}$

$\frac{3.00 \times 10^8}{108 \times 10^6} \texttt{ m} < \lambda < \frac{3.00 \times 10^8}{88.0 \times 10^6} \texttt{ m}$

$\boxed {2.78 \texttt{ m} < \lambda < 3.41 \texttt{ m}}$

$\texttt{ }$

Learn moreSpeed of Wave : linkVelocity of Runner : linkKinetic Energy : linkAcceleration : linkThe Speed of Car : link

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Light

Am radio signals have frequencies between 550 khz and 1600 khz (kilohertz) and travel with a speed o

Answer from: Quest

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Answer from: Quest

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