A person can hear sound waves in the frequency range 20 Hz to 20 kHz. Find the minimum and the maximum wavelengths of sound that is audible to the person. The speed of sound is `360 m s^-1`.

Explanation

To find the minimum and maximum wavelengths of sound that is audible to a person, we can use the relationship between the speed of sound, frequency, and wavelength. The formula we will use is:

\[ V = \lambda \cdot f \]

Where:
- \( V \) is the speed of sound (in meters per second),
- \( \lambda \) is the wavelength (in meters),
- \( f \) is the frequency (in Hertz).

### Step-by-Step Solution:

1. **Identify Given Values**:
- Speed of sound, \( V = 360 \, \text{m/s} \)
- Frequency range: \( f_{\text{min}} = 20 \, \text{Hz} \) and \( f_{\text{max}} = 20 \, \text{kHz} = 20,000 \, \text{Hz} \)

2. **Calculate Minimum Wavelength**:
- The minimum wavelength corresponds to the maximum frequency.
- Using the formula for wavelength:
\[ \lambda_{\text{min}} = \frac{V}{f_{\text{max}}} \]
- Substitute the values:
\[ \lambda_{\text{min}} = \frac{360 \, \text{m/s}}{20,000 \, \text{Hz}} = \frac{360}{20000} = 0.018 \, \text{m} = 18 \, \text{mm} \]

3. **Calculate Maximum Wavelength**:
- The maximum wavelength corresponds to the minimum frequency.
- Using the same formula:
\[ \lambda_{\text{max}} = \frac{V}{f_{\text{min}}} \]
- Substitute the values:
\[ \lambda_{\text{max}} = \frac{360 \, \text{m/s}}{20 \, \text{Hz}} = \frac{360}{20} = 18 \, \text{m} \]

4. **Final Results**:
- Minimum wavelength \( \lambda_{\text{min}} = 18 \, \text{mm} \)
- Maximum wavelength \( \lambda_{\text{max}} = 18 \, \text{m} \)

### Summary:
- The minimum wavelength of sound audible to the person is **18 mm**.
- The maximum wavelength of sound audible to the person is **18 m**.