1. What is the wavelength of a radio wave with a given frequency of 450 kHz?

2. What would be the frequency of a signal with a period of 0.1057?

3. A signal of 5 volts is corrupted by 7 mV rms of noise in a circuit. What is the S/N at this point?

Here are the answers to the questions:

1. **Wavelength of a radio wave with a frequency of 450 kHz:**

The relationship between the speed of a wave (\(v\)), its frequency (\(f\)), and wavelength (\(\lambda\)) is given by:

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

For electromagnetic waves like radio waves, the speed (\(v\)) is the speed of light in a vacuum, which is approximately \(3 \times 10^8 \, \text{m/s}\).

\[
\lambda = \frac{3 \times 10^8}{450 \times 10^3} = \frac{3 \times 10^8}{4.5 \times 10^5} = 666.67 \, \text{meters}
\]

So, the wavelength is **666.67 meters**.

---

2. **Frequency of a signal with a period of 0.1057 seconds:**

The relationship between frequency (\(f\)) and period (\(T\)) is given by:

\[
f = \frac{1}{T}
\]

Substituting \(T = 0.1057 \, \text{seconds}\):

\[
f = \frac{1}{0.1057} \approx 9.46 \, \text{Hz}
\]

So, the frequency is approximately **9.46 Hz**.

---

3. **Signal-to-Noise Ratio (S/N):**

The Signal-to-Noise Ratio (S/N) is the ratio of the signal power to the noise power, typically expressed in decibels (dB). The formula for S/N ratio in decibels is:

\[
S/N \, (\text{dB}) = 20 \log_{10}\left(\frac{V_{\text{signal}}}{V_{\text{noise}}}\right)
\]

Given:
- \( V_{\text{signal}} = 5 \, \text{volts} \)
- \( V_{\text{noise}} = 7 \, \text{mV} = 7 \times 10^{-3} \, \text{volts} \)

\[
S/N = 20 \log_{10}\left(\frac{5}{7 \times 10^{-3}}\right)
\]

\[
S/N = 20 \log_{10}\left(\frac{5}{0.007}\right) = 20 \log_{10}(714.29)
\]

\[
S/N \approx 20 \times 2.854 = 57.08 \, \text{dB}
\]

So, the S/N ratio is approximately **57.08 dB**.

---

Would you like more details on any of these answers? Here are five related questions to expand your understanding:

1. How does the wavelength of a wave change if the frequency increases?
2. What is the relationship between period and wavelength for a given wave?
3. What are the practical implications of having a high or low Signal-to-Noise Ratio (SNR) in communication systems?
4. How can noise in a circuit affect the quality of a signal?
5. How would the wavelength change if the radio wave traveled through a medium other than a vacuum?

**Tip:** When working with logarithmic calculations (like S/N ratio in decibels), remember that a 20 dB increase means the signal power is 10 times stronger, while a 40 dB increase means the signal is 100 times stronger!

Learn how to calculate the wavelength of a radio wave with a frequency of 450 kHz, find the frequency of a signal with a period of 0.1057 seconds, and compute the Signal-to-Noise Ratio (S/N) for a 5V signal with 7 mV of noise. This guide covers wave equations, frequency-period relationships, and logarithmic calculations for S/N ratio, suitable for students in Grades 10-12.

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