The frequency of a fork is `500Hz` . Velocity of sound in air is `350ms^(-1)` . The distance through which sound travel by the time the fork makes `125` vibrations is

Options

A. `87.5m`
B. `700m`
C. `1400m`
D. `1.75m`

Explanation

To solve the problem, we need to find the distance that sound travels while the fork makes 125 vibrations. We can follow these steps:

### Step 1: Determine the time taken for 125 vibrations
The frequency of the fork is given as \( f = 500 \, \text{Hz} \). This means that the fork produces 500 vibrations in one second.

To find the time taken for one vibration, we can use the formula:
\[ \text{Time for one vibration} = \frac{1}{\text{Frequency}} = \frac{1}{500} \, \text{seconds} \]

Now, to find the time for 125 vibrations:
\[ \text{Time for 125 vibrations} = 125 \times \text{Time for one vibration} = 125 \times \frac{1}{500} = \frac{125}{500} \, \text{seconds} \]

### Step 2: Simplify the time calculation
We can simplify \( \frac{125}{500} \):
\[ \frac{125}{500} = \frac{1}{4} \, \text{seconds} \]

### Step 3: Calculate the distance traveled by sound
The velocity of sound in air is given as \( v = 350 \, \text{m/s} \).

Using the formula for distance:
\[ \text{Distance} = \text{Velocity} \times \text{Time} \]
Substituting the values we have:
\[ \text{Distance} = 350 \, \text{m/s} \times \frac{1}{4} \, \text{seconds} \]

### Step 4: Perform the multiplication
Calculating the distance:
\[ \text{Distance} = 350 \times 0.25 = 87.5 \, \text{meters} \]

### Final Answer
The distance through which sound travels by the time the fork makes 125 vibrations is **87.5 meters**.

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