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

Explanation

To solve the problem of finding the frequency of a child's voice given the frequency and wavelength of a man's voice, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between frequency, wavelength, and speed of sound**:
The formula that relates frequency (F), wavelength (λ), and the speed of sound (C) is:
\[ F = \frac{C}{\lambda} \]
where:
- \( F \) is the frequency,
- \( C \) is the speed of sound (approximately 343 m/s in air at room temperature),
- \( \lambda \) is the wavelength.

2. **Identify the known values**:
- For the man's voice:
- Frequency (\( F_M \)) = 300 Hz
- Wavelength (\( \lambda_M \)) = 1 m
- For the child's voice:
- Wavelength (\( \lambda_C \)) = 1.5 m
- Frequency (\( F_C \)) = ? (this is what we need to find)

3. **Set up the equations**:
Using the formula for both the man and the child, we can write:
\[ F_M = \frac{C}{\lambda_M} \quad \text{(1)} \]
\[ F_C = \frac{C}{\lambda_C} \quad \text{(2)} \]

4. **Divide the equations**:
To eliminate \( C \), we can divide equation (1) by equation (2):
\[ \frac{F_M}{F_C} = \frac{C/\lambda_M}{C/\lambda_C} \]
This simplifies to:
\[ \frac{F_M}{F_C} = \frac{\lambda_C}{\lambda_M} \]

5. **Substitute the known values**:
Now we can substitute the known values into the equation:
\[ \frac{300 \, \text{Hz}}{F_C} = \frac{1.5 \, \text{m}}{1 \, \text{m}} \]
This simplifies to:
\[ \frac{300}{F_C} = 1.5 \]

6. **Solve for \( F_C \)**:
Rearranging the equation gives:
\[ F_C = \frac{300}{1.5} \]
Now, performing the division:
\[ F_C = 200 \, \text{Hz} \]

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