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 are in the audible range (20 Hz to 20,000 Hz), we can use the formula for wavelength:

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

where:
- \(\lambda\) is the wavelength,
- \(V\) is the speed of sound in the medium (water in this case),
- \(f\) is the frequency.

Given:
- Speed of sound in water, \(V = 1450 \, \text{m/s}\)
- Minimum frequency, \(f_{\text{min}} = 20 \, \text{Hz}\)
- Maximum frequency, \(f_{\text{max}} = 20000 \, \text{Hz}\)

### Step 1: Calculate the minimum wavelength
The minimum wavelength occurs at the maximum frequency. Therefore, we use the maximum frequency in our calculation.

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

Substituting the values:

\[ \lambda_{\text{min}} = \frac{1450 \, \text{m/s}}{20000 \, \text{Hz}} = \frac{1450}{20000} = 0.0725 \, \text{m} = 72.5 \, \text{mm} \]

### Step 2: Calculate the maximum wavelength
The maximum wavelength occurs at the minimum frequency. Therefore, we use the minimum frequency in our calculation.

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

Substituting the values:

\[ \lambda_{\text{max}} = \frac{1450 \, \text{m/s}}{20 \, \text{Hz}} = \frac{1450}{20} = 72.5 \, \text{m} \]

### Final Results
- Minimum wavelength \(\lambda_{\text{min}} = 72.5 \, \text{mm}\)
- Maximum wavelength \(\lambda_{\text{max}} = 72.5 \, \text{m}\)