Respuesta :
Answer:
a). 100.2 MHz (typical frequency for FM radio broadcasting)
The wavelength of a frequency of 100.2 Mhz is 2.99m.
b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)
The wavelength of a frequency of 1070 khz is 280.3 m.
c. 835.6 MHz (common frequency used for cell phone communication)
The wavelength of a frequency of 835.6 Mhz is 0.35m.
Explanation:
The wavelength can be determined by the following equation:
[tex]c = \lambda \cdot \nu[/tex] (1)
Where c is the speed of light, [tex]\lambda[/tex] is the wavelength and [tex]\nu[/tex] is the frequency.
Notice that since it is electromagnetic radiation, equation 1 can be used. Remember that light propagates in the form of an electromagnetic wave.
a). 100.2 MHz (typical frequency for FM radio broadcasting)
Then, [tex]\lambda[/tex] can be isolated from equation 1:
[tex]\lambda = \frac{c}{\nu}[/tex] (2)
since the value of c is [tex]3x10^{8}m/s[/tex]. It is necessary to express the frequency in units of hertz.
[tex]\nu = 100.2 MHz . \frac{1x10^{6}Hz}{1MHz}[/tex] ⇒ [tex]100200000Hz[/tex]
But [tex]1Hz = s^{-1}[/tex]
[tex]\nu = 100200000s^{-1}[/tex]
Finally, equation 2 can be used:
[tex]\lambda = \frac{3x10^{8}m/s}{100200000s^{-1}}[/tex]
[tex]\lambda = 2.99 m[/tex]
Hence, the wavelength of a frequency of 100.2 Mhz is 2.99m.
b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)
[tex]\nu = 1070kHz . \frac{1000Hz}{1kHz}[/tex] ⇒ [tex]1070000Hz[/tex]
But [tex]1Hz = s^{-1}[/tex]
[tex]\nu = 1070000s^{-1}[/tex]
Finally, equation 2 can be used:
[tex]\lambda = \frac{3x10^{8}m/s}{1070000s^{-1}}[/tex]
[tex]\lambda = 280.3 m[/tex]
Hence, the wavelength of a frequency of 1070 khz is 280.3 m.
c. 835.6 MHz (common frequency used for cell phone communication)
[tex]\nu = 835.6MHz . \frac{1x10^{6}Hz}{1MHz}[/tex] ⇒ [tex]835600000Hz[/tex]
But [tex]1Hz = s^{-1}[/tex]
[tex]\nu = 835600000s^{-1}[/tex]
Finally, equation 2 can be used:
[tex]\lambda = \frac{3x10^{8}m/s}{835600000s^{-1}}[/tex]
[tex]\lambda = 0.35 m[/tex]
Hence, the wavelength of a frequency of 835.6 Mhz is 0.35m.
Following are the calculation of the frequency of the wavelength for each radiation of electromagnetic:
For point a:
[tex]\to f = 100.2\ MHz \ = 1.002 \times 10^{8}\ s^{-1} \\\\[/tex]
Using formula:
[tex]\to \lambda = \frac{c}{f} \\\\[/tex]
[tex]=\frac{(3.0\times 10^{8} \ \frac{m}{s})}{(1.002\times 10^{8}\ s^{-1})}\\\\=\frac{(3.0 \ m)}{(1.002 )}\\\\= 2.994 \ m[/tex]
For point b:
[tex]\to f = 1070\ KHz \ = 1.07 \times 10^{6}\ s^{-1} \\\\[/tex]
Using formula:
[tex]\to \lambda = \frac{c}{f} \\\\[/tex]
[tex]=\frac{(3.0\times 10^{8} \ \frac{m}{s})}{( 1.07 \times 10^{6}\ s^{-1} )}\\\\=\frac{(3.0\times 10^{2} \ m)}{(1.07 )}\\\\= 2.804 \times 10^{2} \ m[/tex]
For point c:
[tex]\to f = 835.6 \ MHz = 8.356 \times 10^{8}\ s^{-1}[/tex]
Using formula:
[tex]\to \lambda = \frac{c}{f} \\\\[/tex]
[tex]=\frac{(3.0\times 10^{8} \ \frac{m}{s})}{( 8.356\times 10^{8}\ s^{-1} )}\\\\=\frac{(3.0\ m)}{(8.356 )}\\\\= 0.3590 \ m[/tex]
Therefore, the final answer is "2.994 m, 2.804× 10² m, and 0.35900 m"
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