An insect makes sound that is higher than the maximum audible frequency of human beings. Given that speed of sound in air is approximately 340 m `s^(-1)`, which of the following could be the wavelength of the sound ?

Options

A. `1. 4 xx 10^(-2) m`
B. `3.6 xx 10^(-2)m`
C. `3.2 xx 10^(-1) m`
D. 5. 0 m

Explanation

To solve the problem, we need to find the wavelength of the sound produced by an insect that emits sound at a frequency higher than the maximum audible frequency of human beings, which is 20,000 Hz. The speed of sound in air is given as 340 m/s.

### Step-by-Step Solution:

1. **Identify the relationship between speed, frequency, and wavelength**:
The relationship can be expressed using the formula:
\[ v = f \cdot \lambda \]
where:
- \( v \) is the speed of sound (340 m/s),
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.

2. **Determine the frequency**:
Since the insect makes sound at a frequency higher than 20,000 Hz, we can denote the frequency as:
\[ f > 20,000 \text{ Hz} \]

3. **Rearranging the formula**:
We can rearrange the formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]

4. **Substituting the values**:
Since we know that \( f > 20,000 \text{ Hz} \), we can substitute the values into the equation:
\[ \lambda < \frac{340 \text{ m/s}}{20,000 \text{ Hz}} \]

5. **Calculating the wavelength**:
Now, we perform the calculation:
\[ \lambda < \frac{340}{20,000} = 0.017 \text{ m} \]
This can be expressed in scientific notation:
\[ \lambda < 1.7 \times 10^{-2} \text{ m} \]

6. **Identifying the correct option**:
We need to find a wavelength that is less than \( 1.7 \times 10^{-2} \text{ m} \). If we have options, we will select the one that meets this criterion.

### Conclusion:
The wavelength of the sound produced by the insect must be less than \( 1.7 \times 10^{-2} \text{ m} \). Therefore, among the options provided, the correct answer would be the one that is less than this value.