If the frequency of a tuning fork is 400 Hz, how far will the sound travel when the fork makes 60 vibrations? Given, velocity of sound = 320 `ms^(-1)`

Options

A. 96 m
B. 48 m
C. 24 m
D. 12 m

Explanation

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

### Step 1: Understand the given information
- Frequency of the tuning fork (f) = 400 Hz
- Number of vibrations (n) = 60
- Velocity of sound (v) = 320 m/s

### Step 2: Calculate the wavelength (λ)
The relationship between velocity (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \times \lambda \]

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

Substituting the values:
\[ \lambda = \frac{320 \, \text{m/s}}{400 \, \text{Hz}} \]

### Step 3: Perform the calculation for wavelength
Calculating the above expression:
\[ \lambda = \frac{320}{400} = \frac{4}{5} \, \text{m} \]
So, the wavelength (λ) is 0.8 m.

### Step 4: Calculate the total distance traveled for 60 vibrations
The total distance (d) traveled by the sound when the tuning fork makes 60 vibrations can be calculated using the formula:
\[ d = n \times \lambda \]

Substituting the values:
\[ d = 60 \times \frac{4}{5} \]

### Step 5: Perform the calculation for distance
Calculating the above expression:
\[ d = 60 \times 0.8 = 48 \, \text{m} \]

### Final Answer
The sound will travel a distance of **48 meters** when the tuning fork makes 60 vibrations.

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