Waves of frequency `1000 Hz` are produced in a Kundt's tube . The total distance between `6` successive nodes is `82.5 cm`. The speed of sound in the gas filled in the tube is

Options

A. `33 cm//s`
B. `33 m//s`
C. `330 m//s`
D. `660 m//s`

Explanation

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). If we have 6 successive nodes, we can visualize them as follows:

- Node 1 to Node 2: λ/2
- Node 2 to Node 3: λ/2
- Node 3 to Node 4: λ/2
- Node 4 to Node 5: λ/2
- Node 5 to Node 6: λ/2

Thus, the distance between 6 nodes consists of 5 segments of λ/2.

### Step 2: Calculate the total distance between nodes
Given that the total distance between 6 successive nodes is 82.5 cm, we can express this as:
\[ \text{Total distance} = 5 \times \frac{\lambda}{2} \]
So, we can write:
\[ 82.5 \text{ cm} = 5 \times \frac{\lambda}{2} \]

### Step 3: Solve for the wavelength (λ)
Rearranging the equation to solve for λ:
\[ \lambda = \frac{82.5 \text{ cm} \times 2}{5} \]
Calculating this gives:
\[ \lambda = \frac{165 \text{ cm}}{5} = 33 \text{ cm} \]

### Step 4: Convert the wavelength to meters
Since we need the wavelength in meters for the speed calculation, we convert 33 cm to meters:
\[ \lambda = 33 \text{ cm} = 0.33 \text{ m} \]

### Step 5: Use the speed formula
The speed of sound (v) can be calculated using the formula:
\[ v = f \times \lambda \]
Where:
- \( f \) is the frequency (1000 Hz)
- \( \lambda \) is the wavelength (0.33 m)

Substituting the values:
\[ v = 1000 \text{ Hz} \times 0.33 \text{ m} = 330 \text{ m/s} \]

### Final Answer
The speed of sound in the gas filled in the tube is **330 m/s**.

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