Answer : The wavelength of the radio waves is [tex]6.2\times 10^{-2}m[/tex]
Explanation : Given,
Frequency = [tex]4.8\times 10^9 Hz[/tex]
Wave speed = [tex]3.0\times 10^8 m/s[/tex]
As we know that the speed of a wave is related to its frequency and wavelength.
Formula used:
[tex]\nu =f\times \lambda[/tex]
where,
[tex]\nu[/tex] is the wave speed in metres per second, (m/s )
f is the frequency in hertz, (Hz )
[tex]\lambda[/tex] is the wavelength in metres, (m)
Now putting all the given values in the above formula, we get:
[tex]3.0\times 10^8 m/s=(4.8\times 10^9 Hz)\times \lambda[/tex]
[tex]\lambda=6.2\times 10^{-2}m[/tex]
Therefore, the wavelength of the radio waves is [tex]6.2\times 10^{-2}m[/tex]
The wavelength of the radio waves is 0.063 m
From the question, we are to determine the wavelength of the radio waves.
From the formula,
[tex]c = f \lambda[/tex]
Then, we can write that
[tex]\lambda = \frac{c}{f} [/tex]
Where c is the wave speed
[tex]f [/tex] is the frequency
and [tex]\lambda [/tex] is the wavelength
From the given information,
[tex]f = 4.8 \times 10^{9} \ Hz [/tex]
and [tex]c = 3.0 \times 10^{8} \ m/s[/tex]
Putting the parameters into the formula, we get
[tex]\lambda = \frac{3.0 \times 10^{8} }{4.8\times 10^{9} } [/tex]
[tex]\lambda = 0.625 \times 10^{-1} [/tex]
[tex]\lambda = 0.0625 \ m [/tex]
[tex]\lambda = 0.063 \ m [/tex] (to 2 significant figures)
Hence, the wavelength of the radio waves is 0.063 m
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