Two sounds are heard at the end of an iron rod 5 km long at an interval of 14 seconds, when a source of sound is placed at the other end of the rod. The velocity of sound in air is 330 m/s. the velocity of sound in iron is aproximately

Options

A. 4348 m/s
B. 1500 m/s
C. 2200 m/s
D. 330 m/s

Answer

To find the velocity of sound in iron, we can follow these steps:

### Step 1: Understand the problem
We have a 5 km long iron rod, and two sounds are heard at the end of the rod at an interval of 14 seconds. The speed of sound in air is given as 330 m/s. We need to find the speed of sound in iron.

### Step 2: Convert the distance from kilometers to meters
The length of the iron rod is given as 5 km. We need to convert this to meters:
\[ \text{Distance} = 5 \text{ km} = 5000 \text{ m} \]

### Step 3: Calculate the time taken for sound to travel through air
Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values for sound in air:
\[ \text{Time in air} = \frac{5000 \text{ m}}{330 \text{ m/s}} \approx 15.15 \text{ seconds} \]

### Step 4: Determine the time taken for sound to travel through iron
Since the two sounds are heard 14 seconds apart, we can find the time taken for sound to travel through iron:
\[ \text{Time in iron} = \text{Time in air} - 14 \text{ seconds} \]
Substituting the calculated time:
\[ \text{Time in iron} = 15.15 \text{ seconds} - 14 \text{ seconds} = 1.15 \text{ seconds} \]

### Step 5: Calculate the velocity of sound in iron
Now, we can find the speed of sound in iron using the formula:
\[ \text{Velocity} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ \text{Velocity in iron} = \frac{5000 \text{ m}}{1.15 \text{ seconds}} \approx 4347.83 \text{ m/s} \]

### Conclusion
The velocity of sound in iron is approximately \( 4347.83 \text{ m/s} \).

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