A station broadcasts an AM radio wave whose frequency is 1230 x 10 Hz (1230 kHz on the dial) and an FM radio wave whose frequency is 91.9 x 10 Hz (91.9 MHz on the dial). Find the distance between adjacent crests in each wave.

To find the distance between adjacent crests in a wave, we need to calculate the **wavelength**. The formula for the wavelength (\( \lambda \)) is:

\[
\lambda = \frac{c}{f}
\]

Where:
- \( c \) is the speed of light, which is approximately \( 3.0 \times 10^8 \, \text{m/s} \),
- \( f \) is the frequency of the wave.

### 1. AM Radio Wave Wavelength
Given the frequency for the AM radio wave:

\[
f_{\text{AM}} = 1230 \times 10^3 \, \text{Hz} = 1.230 \times 10^6 \, \text{Hz}
\]

Using the formula:

\[
\lambda_{\text{AM}} = \frac{3.0 \times 10^8}{1.230 \times 10^6}
\]

\[
\lambda_{\text{AM}} \approx 243.9 \, \text{m}
\]

### 2. FM Radio Wave Wavelength
Given the frequency for the FM radio wave:

\[
f_{\text{FM}} = 91.9 \times 10^6 \, \text{Hz} = 9.19 \times 10^7 \, \text{Hz}
\]

Using the formula:

\[
\lambda_{\text{FM}} = \frac{3.0 \times 10^8}{9.19 \times 10^7}
\]

\[
\lambda_{\text{FM}} \approx 3.26 \, \text{m}
\]

### Final Answers:
- The wavelength of the AM radio wave is approximately \( 243.9 \, \text{m} \).
- The wavelength of the FM radio wave is approximately \( 3.26 \, \text{m} \).

Would you like more details or clarifications on the process?

### Related Questions:
1. How does the wavelength affect radio signal strength?
2. Why do AM and FM waves have different frequencies?
3. How does wavelength relate to the energy of the wave?
4. What is the relationship between frequency and wavelength?
5. How does the speed of light play a role in wave propagation?

**Tip:** Higher frequencies (like FM) correspond to shorter wavelengths, leading to different propagation characteristics.

Learn how to calculate the wavelength of AM and FM radio waves with frequencies of 1230 kHz and 91.9 MHz, respectively. This solution involves applying the wavelength formula (λ = c / f), where c is the speed of light and f is the frequency. Suitable for high school physics students (Grades 9-12).

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