In a Kundt's tube , the length of the iron rod is `1 m`. The stationary waves frequency `2500 Hz` are produced in it. The velocity of sound in iron is

Options

A. `1250 m//s`
B. `2500 m//s`
C. `5000 m//s`
D. `10,000 m//s`

Explanation

To find the velocity of sound in iron using the information provided about the Kundt's tube, we can follow these steps:

### Step 1: Understand the relationship between wavelength, frequency, and velocity
The velocity of a wave (V) is related to its frequency (f) and wavelength (λ) by the equation:
\[ V = f \cdot \lambda \]

### Step 2: Determine the wavelength
In a Kundt's tube, when stationary waves are formed, the distance between a node and an antinode is \( \frac{\lambda}{4} \). Since the tube has both ends fixed, the length of the tube can be represented as:
\[ L = \frac{n \lambda}{2} \]
where \( n \) is the number of wavelengths fitting into the length of the tube. For the fundamental mode (first harmonic), \( n = 1 \):
\[ L = \frac{1 \lambda}{2} \]
Given that the length of the iron rod (tube) is 1 meter:
\[ 1 = \frac{1 \lambda}{2} \]
This implies:
\[ \lambda = 2 \text{ meters} \]

### Step 3: Use the frequency to find the velocity
Now that we have the wavelength, we can substitute the values into the wave velocity equation. The frequency (f) is given as 2500 Hz:
\[ V = f \cdot \lambda \]
Substituting the known values:
\[ V = 2500 \, \text{Hz} \cdot 2 \, \text{m} \]
\[ V = 5000 \, \text{m/s} \]

### Conclusion
The velocity of sound in iron is:
\[ V = 5000 \, \text{m/s} \]

### Final Answer
The velocity of sound in iron is **5000 m/s**.

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