The frequency of a tuning fork is `256Hz` . The velocity of sound in air is `344ms^(-1)`.The distance travelled (in metres) by the sound during the time in which the tuning fork completes `32`vibrations

Options

A. `21`
B. `43`
C. `86`
D. `129`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given data
- Frequency of the tuning fork (f) = 256 Hz
- Velocity of sound in air (v) = 344 m/s
- Number of vibrations (n) = 32

### Step 2: Calculate the wavelength (λ)
We can use the formula that relates the velocity of sound, frequency, and wavelength:
\[ v = f \cdot \lambda \]
Rearranging the formula to find the wavelength (λ):
\[ \lambda = \frac{v}{f} \]

### Step 3: Substitute the values into the wavelength formula
Substituting the values we have:
\[ \lambda = \frac{344 \, \text{m/s}}{256 \, \text{Hz}} \]

### Step 4: Perform the calculation for wavelength
Calculating the above expression:
\[ \lambda = 1.34375 \, \text{m} \]
We can round this to:
\[ \lambda \approx 1.344 \, \text{m} \]

### Step 5: Calculate the distance travelled by sound during 32 vibrations
The distance travelled by sound (d) during n vibrations can be calculated using the formula:
\[ d = n \cdot \lambda \]
Substituting the values:
\[ d = 32 \cdot 1.344 \, \text{m} \]

### Step 6: Perform the multiplication
Calculating the distance:
\[ d = 42.976 \, \text{m} \]
We can round this to:
\[ d \approx 43 \, \text{m} \]

### Final Answer
The distance travelled by the sound during the time in which the tuning fork completes 32 vibrations is approximately **43 meters**.

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