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. `330 m//s`
B. `340 m//s`
C. `350 m//s`
D. `300m//s`

Answer

To find the speed of sound in the gas filled in the Kundt's tube, we can follow these steps:

### Step 1: Understand the relationship between nodes and wavelength
In a standing wave, the distance between two successive nodes is equal to half the wavelength (λ/2). Therefore, if we have 6 successive nodes, the distance covered is 5 half-wavelengths (5λ/2).

### Step 2: Set up the equation for the distance between nodes
Given that the total distance between 6 successive nodes is 85 cm, we can express this mathematically:
\[ \frac{5\lambda}{2} = 85 \text{ cm} \]

### Step 3: Solve for the wavelength (λ)
To find the wavelength, we can rearrange the equation:
\[ 5\lambda = 85 \times 2 \]
\[ 5\lambda = 170 \text{ cm} \]
Now, divide by 5:
\[ \lambda = \frac{170 \text{ cm}}{5} = 34 \text{ cm} \]
Convert centimeters to meters (1 cm = 0.01 m):
\[ \lambda = 34 \text{ cm} \times 0.01 = 0.34 \text{ m} \]

### Step 4: Use the speed of sound formula
The speed of sound (v) can be calculated using the formula:
\[ v = f \times \lambda \]
where \(f\) is the frequency. We are given that the frequency \(f = 1000 \text{ Hz}\).

### Step 5: Calculate the speed of sound
Substituting the values into the formula:
\[ v = 1000 \text{ Hz} \times 0.34 \text{ m} \]
\[ v = 340 \text{ m/s} \]

### Conclusion
The speed of sound in the gas filled in the tube is **340 m/s**.

---