Find the minimum and maximum wavelengths of sound in water that is in the audible range (20-20000 Hz) for an average human ear. Speed of sound in water `= 1450 m s^-1`.

Explanation

To find the minimum and maximum wavelengths of sound in water that fall within the audible range (20 Hz to 20,000 Hz), we can use the formula that relates the speed of sound, frequency, and wavelength:

\[ v = f \cdot \lambda \]

Where:
- \( v \) is the speed of sound in water (1450 m/s),
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.

### Step 1: Identify the maximum frequency
The maximum frequency in the audible range is 20,000 Hz.

### Step 2: Calculate the minimum wavelength
Using the formula for wavelength:

\[ \lambda_{\text{min}} = \frac{v}{f_{\text{max}}} \]

Substituting the values:

\[ \lambda_{\text{min}} = \frac{1450 \, \text{m/s}}{20000 \, \text{Hz}} \]

\[ \lambda_{\text{min}} = \frac{1450}{20000} \]

\[ \lambda_{\text{min}} = 0.0725 \, \text{m} \]

### Step 3: Identify the minimum frequency
The minimum frequency in the audible range is 20 Hz.

### Step 4: Calculate the maximum wavelength
Using the formula for wavelength:

\[ \lambda_{\text{max}} = \frac{v}{f_{\text{min}}} \]

Substituting the values:

\[ \lambda_{\text{max}} = \frac{1450 \, \text{m/s}}{20 \, \text{Hz}} \]

\[ \lambda_{\text{max}} = \frac{1450}{20} \]

\[ \lambda_{\text{max}} = 72.5 \, \text{m} \]

### Final Results
- Minimum wavelength (\( \lambda_{\text{min}} \)): 0.0725 m (or 7.25 cm)
- Maximum wavelength (\( \lambda_{\text{max}} \)): 72.5 m