The frequency of a man's voice is 300 Hz and its wavelength is 1 meter. If the wavelength of a child's voice is 1.5 m, then the frequency of the child's voice is"

Options

A. `200 Hz`
B. `150 Hz`
C. `400 Hz`
D. `350 Hz`

Explanation

To find the frequency of the child's voice given the frequency and wavelength of the man's voice, we can use the relationship between frequency (f), wavelength (λ), and the speed of sound (v).

### Step-by-Step Solution:

1. **Understand the relationship**: The speed of sound in a medium is given by the formula:
\[ v = f \times \lambda \]
where \( v \) is the speed of sound, \( f \) is the frequency, and \( \lambda \) is the wavelength.

2. **Identify known values**:
- For the man's voice:
- Frequency \( f_1 = 300 \, \text{Hz} \)
- Wavelength \( \lambda_1 = 1 \, \text{m} \)
- For the child's voice:
- Wavelength \( \lambda_2 = 1.5 \, \text{m} \)
- Frequency \( f_2 \) (unknown)

3. **Calculate the speed of sound using the man's voice**:
\[ v = f_1 \times \lambda_1 = 300 \, \text{Hz} \times 1 \, \text{m} = 300 \, \text{m/s} \]

4. **Use the speed of sound to find the frequency of the child's voice**:
Since the speed of sound remains constant in the same medium, we can set up the equation:
\[ v = f_2 \times \lambda_2 \]
Substituting the known values:
\[ 300 \, \text{m/s} = f_2 \times 1.5 \, \text{m} \]

5. **Solve for \( f_2 \)**:
\[ f_2 = \frac{300 \, \text{m/s}}{1.5 \, \text{m}} = 200 \, \text{Hz} \]

6. **Conclusion**: The frequency of the child's voice is \( 200 \, \text{Hz} \).

### Final Answer:
The frequency of the child's voice is **200 Hz**.