A sound wave of frequency 1 kHz takes (10/3) seconds to travel a distance of 1 km. Then its wavelength would be _____

Options

A. 20 cm
B. 200 cm
C. 300 cm
D. 30 cm

Explanation

To find the wavelength of a sound wave given its frequency and the time taken to travel a certain distance, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Frequency (f) = 1 kHz = 1000 Hz (since 1 kHz = 1000 Hz)
- Time (t) = \( \frac{10}{3} \) seconds
- Distance (d) = 1 km = 1000 meters (since 1 km = 1000 m)

2. **Calculate the Speed of Sound:**
- Speed (v) is calculated using the formula:
\[ v = \frac{d}{t} \]
- Substituting the values:
\[ v = \frac{1000 \text{ m}}{\frac{10}{3} \text{ s}} = 1000 \times \frac{3}{10} = 300 \text{ m/s} \]

3. **Use the Wave Equation to Find Wavelength:**
- The relationship between speed (v), frequency (f), and wavelength (λ) is given by:
\[ v = f \times \lambda \]
- Rearranging the formula to find wavelength (λ):
\[ \lambda = \frac{v}{f} \]
- Substituting the known values:
\[ \lambda = \frac{300 \text{ m/s}}{1000 \text{ Hz}} = \frac{300}{1000} = \frac{3}{10} \text{ m} \]

4. **Convert Wavelength to Centimeters:**
- Since the answer is required in centimeters, convert meters to centimeters:
\[ \lambda = \frac{3}{10} \text{ m} \times 100 \text{ cm/m} = 30 \text{ cm} \]

5. **Final Answer:**
- The wavelength of the sound wave is **30 cm**.