On producing the waves of frequency 1000 Hz in a kundt's tube the total distance between 6 successive nodes n 85 cm. Speed of sound in the gas filled in the tude is

Options

A. `300 ms^(-1)`
B. `350 ms^(-1)`
C. `340 ms^(-1)`
D. `330 ms^(-1)`

Answer

To solve the problem, we need to find the speed of sound in the gas filled in the Kundt's tube. We are given the frequency of the waves and the total distance between six successive nodes.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Frequency (f) = 1000 Hz
- Distance between 6 successive nodes = 85 cm

2. **Understanding Nodes in a Wave:**
- In a standing wave, nodes are points where there is no displacement. The distance between two successive nodes is half the wavelength (λ).
- Therefore, the distance between 6 successive nodes can be expressed in terms of the wavelength.

3. **Calculate the Distance Between Nodes:**
- The distance between 6 successive nodes corresponds to 5 wavelengths (since the first node is counted as the starting point).
- Hence, we can write:
\[ \text{Distance between 6 nodes} = 5 \times \left(\frac{\lambda}{2}\right) = \frac{5\lambda}{2} \]
- Setting this equal to the given distance:
\[ \frac{5\lambda}{2} = 85 \text{ cm} \]

4. **Solve for Wavelength (λ):**
- Rearranging the equation gives:
\[ 5\lambda = 170 \text{ cm} \]
\[ \lambda = \frac{170 \text{ cm}}{5} = 34 \text{ cm} \]
- Converting this to meters:
\[ \lambda = 0.34 \text{ m} \]

5. **Calculate the Speed of Sound (v):**
- The speed of sound in the gas can be calculated using the formula:
\[ v = f \times \lambda \]
- Substituting the values:
\[ v = 1000 \text{ Hz} \times 0.34 \text{ m} = 340 \text{ m/s} \]

6. **Final Answer:**
- The speed of sound in the gas is **340 m/s**.