How far does sound travel in air when a tuning fork of frequency 480 Hz completes 50 vibrations. Velocity of sound is 348 `ms^(-1)`.

Answer

To solve the problem of how far sound travels in air when a tuning fork of frequency 480 Hz completes 50 vibrations, we can follow these steps:

### Step 1: Understand the relationship between frequency, wavelength, and velocity
The relationship between the velocity of sound (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \times \lambda \]

### Step 2: Rearrange the formula to find the wavelength
We can rearrange the formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]

### Step 3: Substitute the given values into the equation
We know:
- Velocity of sound, \( v = 348 \, \text{m/s} \)
- Frequency of the tuning fork, \( f = 480 \, \text{Hz} \)

Substituting these values into the equation for wavelength:
\[ \lambda = \frac{348 \, \text{m/s}}{480 \, \text{Hz}} \]

### Step 4: Calculate the wavelength
Now, perform the calculation:
\[ \lambda = \frac{348}{480} \approx 0.725 \, \text{m} \]

### Step 5: Calculate the distance traveled for 50 vibrations
Since one vibration corresponds to one wavelength, the distance traveled by sound for 50 vibrations is:
\[ \text{Distance} = 50 \times \lambda \]
\[ \text{Distance} = 50 \times 0.725 \, \text{m} \]

### Step 6: Perform the final calculation
Now, calculate the distance:
\[ \text{Distance} = 50 \times 0.725 = 36.25 \, \text{m} \]

### Final Answer
The sound travels approximately **36.25 meters** in air when the tuning fork completes 50 vibrations.

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