Question

question 8 (1 point)
a radio station has a frequency of 90.9 megahertz (9.09e7 hz). what is the wavelength of the radio waves the station emits from its radio tower?
_______ m (round to the tenths place and dont put any spaces between the e and the numbers, e.g 4.5e-23)
blank 1:

question 9 (1 point)
an x - ray has a wavelength of 5 nanometers (5.0×10⁻⁹ m). what is the frequency of x - rays?
_______ hz
blank 1:

Explanation:

Step1: Recall wave speed formula

The relationship between wave speed ($c$), frequency ($f$), and wavelength ($\lambda$) is $c = \lambda f$, where $c = 3.00 \times 10^8 \, \text{m/s}$ (speed of electromagnetic waves in vacuum). Rearranged for wavelength: $\lambda = \frac{c}{f}$

Step2: Solve Question 8

Substitute $c = 3.00 \times 10^8 \, \text{m/s}$ and $f = 9.09 \times 10^7 \, \text{Hz}$:
$$\lambda = \frac{3.00 \times 10^8}{9.09 \times 10^7} \approx 3.3 \, \text{m}$$

Step3: Rearrange formula for frequency

For Question 9, rearrange $c = \lambda f$ to $f = \frac{c}{\lambda}$

Step4: Solve Question 9

Substitute $c = 3.00 \times 10^8 \, \text{m/s}$ and $\lambda = 5.0 \times 10^{-9} \, \text{m}$:
$$f = \frac{3.00 \times 10^8}{5.0 \times 10^{-9}} = 6.0 \times 10^{16} = 6.0\text{E16} \, \text{Hz}$$

Answer:

3.3 m
6.0E16 Hz