How far does the sound travel in air when a tuning fork of frequency 500 Hz completes 25 vibrations ? Velocity of sound in air is 332 `ms^(-1)`.

Answer

To solve the problem of how far sound travels in air when a tuning fork of frequency 500 Hz completes 25 vibrations, we can follow these steps:

### Step 1: Understand the relationship between frequency, wavelength, and velocity
The speed of sound in air is given by the formula:
\[ v = f \times \lambda \]
where:
- \( v \) is the velocity of sound (in meters per second),
- \( f \) is the frequency (in hertz),
- \( \lambda \) is the wavelength (in meters).

### Step 2: Calculate the wavelength
Given:
- Velocity of sound, \( v = 332 \, \text{m/s} \)
- Frequency, \( f = 500 \, \text{Hz} \)

We can rearrange the formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]

Substituting the values:
\[ \lambda = \frac{332 \, \text{m/s}}{500 \, \text{Hz}} = 0.664 \, \text{m} \]

### Step 3: Calculate the total distance traveled for 25 vibrations
Since one vibration corresponds to one wavelength, the distance traveled for 25 vibrations is:
\[ \text{Total Distance} = \text{Number of Vibrations} \times \text{Wavelength} \]

Substituting the values:
\[ \text{Total Distance} = 25 \times 0.664 \, \text{m} = 16.6 \, \text{m} \]

### Final Answer
The sound travels a distance of **16.6 meters** in air when the tuning fork completes 25 vibrations.

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