The wavelength of a wave is determined by its wave number $k$, where $k = \frac{2\pi}{\lambda}$. The relationship between the wave number and the wavelength is:

$\lambda = \frac{2\pi}{k}$

From the given equations:

The wave number is: $k = 54.6 \, \text{m}^{-1}$

Calculate the wavelength:

Convert $k$ to centimeters by noting $1 \, \text{m}^{-1} = 100 \, \text{cm}^{-1}$: $k = 54.6 \, \text{m}^{-1} = 5460 \, \text{cm}^{-1}$

Now calculate $\lambda$: $\lambda = \frac{2\pi}{k} = \frac{2\pi}{5460}$

$\lambda \approx \frac{6.2832}{5460} \approx 0.00115 \, \text{cm}$

Final Answer:

The wavelength is approximately 0.00115 cm.

Would you like me to explain the steps further, or assist with the next part? Here are some related questions for deeper exploration:

1. How does the phase difference affect the resultant wave?
2. What is the observed amplitude of the resultant wave?
3. How do you derive the relationship between $k$, $\lambda$, and $\omega$?
4. How do two interfering waves produce constructive and destructive interference?
5. What is the importance of phase constants in wave interference?

Tip: Always confirm that units are consistent before calculations to avoid conversion errors.