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 a person can hear, we will use the relationship between the speed of sound (v), frequency (f), and wavelength (λ). The formula is given by:

\[ v = f \cdot \lambda \]

Where:
- \( v \) is the speed of sound,
- \( f \) is the frequency of the sound,
- \( \lambda \) is the wavelength.

### Step 1: Identify the given values
- Speed of sound, \( v = 360 \, \text{m/s} \)
- Minimum frequency, \( f_1 = 20 \, \text{Hz} \)
- Maximum frequency, \( f_2 = 20 \, \text{kHz} = 20,000 \, \text{Hz} \)

### Step 2: Calculate the maximum wavelength (λ_max)
The maximum wavelength corresponds to the minimum frequency (20 Hz). We can rearrange the formula to solve for wavelength:

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

Substituting the values for maximum wavelength:

\[ \lambda_{\text{max}} = \frac{360 \, \text{m/s}}{20 \, \text{Hz}} \]

Calculating this gives:

\[ \lambda_{\text{max}} = \frac{360}{20} = 18 \, \text{m} \]

### Step 3: Calculate the minimum wavelength (λ_min)
The minimum wavelength corresponds to the maximum frequency (20 kHz). Using the same formula:

\[ \lambda_{\text{min}} = \frac{v}{f} \]

Substituting the values for minimum wavelength:

\[ \lambda_{\text{min}} = \frac{360 \, \text{m/s}}{20,000 \, \text{Hz}} \]

Calculating this gives:

\[ \lambda_{\text{min}} = \frac{360}{20,000} = 0.018 \, \text{m} = 18 \, \text{mm} \]

### Final Results
- Maximum Wavelength (λ_max) = 18 m
- Minimum Wavelength (λ_min) = 18 mm