A tuning fork vibrates with a frequency of 256. If the speed of sound is `345.6 ms^(-1)`., Find the wavelength and the distance, which the sound travels during the time, the fork makes 60 vibrations.

Options

A. 1.35 m, 81 m
B. 1.40 m, 84 m
C. 1.45 m, 87 m
D. 1.55 m, 93 m

Answer

To solve the problem, we need to find the wavelength of the sound produced by the tuning fork and the distance the sound travels during 60 vibrations.

### Step 1: Calculate the Wavelength
We know the relationship between speed (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \times \lambda \]

From this, we can rearrange the formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]

Given:
- Speed of sound, \( v = 345.6 \, \text{m/s} \)
- Frequency of the tuning fork, \( f = 256 \, \text{Hz} \)

Now substituting the values into the formula:
\[ \lambda = \frac{345.6 \, \text{m/s}}{256 \, \text{Hz}} \]

Calculating this gives:
\[ \lambda = 1.35 \, \text{m} \]

### Step 2: Calculate the Distance for 60 Vibrations
The distance traveled by sound in 60 vibrations can be calculated using the wavelength:
\[ \text{Distance} = \text{Number of Vibrations} \times \text{Wavelength} \]

Given that the number of vibrations is 60:
\[ \text{Distance} = 60 \times \lambda \]
\[ \text{Distance} = 60 \times 1.35 \, \text{m} \]

Calculating this gives:
\[ \text{Distance} = 81 \, \text{m} \]

### Final Results
- Wavelength \( \lambda = 1.35 \, \text{m} \)
- Distance traveled in 60 vibrations = 81 m