Answer :
We are given the frequency of radio waves as
[tex]$$
f = 99.7 \times 10^6 \text{ Hz}
$$[/tex]
and the speed of light as
[tex]$$
c = 3.0 \times 10^8 \text{ m/s}.
$$[/tex]
The relationship between the speed of light, frequency, and wavelength is given by the formula:
[tex]$$
c = f \lambda,
$$[/tex]
where [tex]$\lambda$[/tex] is the wavelength.
Step 1: Solve for the wavelength [tex]$\lambda$[/tex]
Rearrange the formula to isolate [tex]$\lambda$[/tex]:
[tex]$$
\lambda = \frac{c}{f}.
$$[/tex]
Step 2: Substitute the known values
Substitute [tex]$c$[/tex] and [tex]$f$[/tex] into the equation:
[tex]$$
\lambda = \frac{3.0 \times 10^8 \text{ m/s}}{99.7 \times 10^6 \text{ Hz}}.
$$[/tex]
Step 3: Simplify the expression
First, we can simplify the powers of ten:
[tex]$$
\lambda = \frac{3.0}{99.7} \times 10^{8-6} \text{ m} = \frac{3.0}{99.7} \times 10^2 \text{ m}.
$$[/tex]
Since [tex]$10^2 = 100$[/tex], the equation becomes:
[tex]$$
\lambda = \frac{3.0 \times 100}{99.7} \text{ m} = \frac{300}{99.7} \text{ m}.
$$[/tex]
Step 4: Calculate the numerical result
Dividing [tex]$300$[/tex] by [tex]$99.7$[/tex], we obtain:
[tex]$$
\lambda \approx 3.009 \text{ m}.
$$[/tex]
Final Answer:
The wavelength of the radio waves is approximately
[tex]$$
3.01 \text{ m}.
$$[/tex]
[tex]$$
f = 99.7 \times 10^6 \text{ Hz}
$$[/tex]
and the speed of light as
[tex]$$
c = 3.0 \times 10^8 \text{ m/s}.
$$[/tex]
The relationship between the speed of light, frequency, and wavelength is given by the formula:
[tex]$$
c = f \lambda,
$$[/tex]
where [tex]$\lambda$[/tex] is the wavelength.
Step 1: Solve for the wavelength [tex]$\lambda$[/tex]
Rearrange the formula to isolate [tex]$\lambda$[/tex]:
[tex]$$
\lambda = \frac{c}{f}.
$$[/tex]
Step 2: Substitute the known values
Substitute [tex]$c$[/tex] and [tex]$f$[/tex] into the equation:
[tex]$$
\lambda = \frac{3.0 \times 10^8 \text{ m/s}}{99.7 \times 10^6 \text{ Hz}}.
$$[/tex]
Step 3: Simplify the expression
First, we can simplify the powers of ten:
[tex]$$
\lambda = \frac{3.0}{99.7} \times 10^{8-6} \text{ m} = \frac{3.0}{99.7} \times 10^2 \text{ m}.
$$[/tex]
Since [tex]$10^2 = 100$[/tex], the equation becomes:
[tex]$$
\lambda = \frac{3.0 \times 100}{99.7} \text{ m} = \frac{300}{99.7} \text{ m}.
$$[/tex]
Step 4: Calculate the numerical result
Dividing [tex]$300$[/tex] by [tex]$99.7$[/tex], we obtain:
[tex]$$
\lambda \approx 3.009 \text{ m}.
$$[/tex]
Final Answer:
The wavelength of the radio waves is approximately
[tex]$$
3.01 \text{ m}.
$$[/tex]
