If a vibrating tuning fork of frequency `255Hz` is approaching with a velocity `4m//s` perpendicular to a wall. The number of beats produced per sec is (speed of sound in air `=340m//s`)

Options

A. `3`
B. `4`
C. `5`
D. `6`

Explanation

To solve the problem, we need to find the number of beats produced per second when a tuning fork of frequency 255 Hz is approaching a wall at a velocity of 4 m/s. The speed of sound in air is given as 340 m/s.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of the tuning fork (ν) = 255 Hz
- Velocity of the tuning fork (vs) = 4 m/s (approaching the wall)
- Speed of sound in air (v) = 340 m/s

2. **Determine the Apparent Frequency (ν'):**
When the source of sound (tuning fork) is moving towards a stationary observer (the wall), the apparent frequency can be calculated using the formula:
\[ \nu' = \nu \left( \frac{v}{v - vs} \right) \]
Here, since the tuning fork is approaching the wall, we subtract the source velocity from the speed of sound.

3. **Substituting the Values:**
\[ \nu' = 255 \left( \frac{340}{340 - 4} \right) \]
Simplifying the denominator:
\[ 340 - 4 = 336 \]
Thus, we have:
\[ \nu' = 255 \left( \frac{340}{336} \right) \]

4. **Calculating the Apparent Frequency:**
\[ \nu' = 255 \times 1.00714 \approx 258 \text{ Hz} \]
(Using a calculator, \( \frac{340}{336} \approx 1.00714 \))

5. **Calculate the Number of Beats:**
The number of beats produced per second is the difference between the apparent frequency and the original frequency:
\[ \text{Number of beats} = \nu' - \nu = 258 \text{ Hz} - 255 \text{ Hz} = 3 \text{ Hz} \]

### Final Answer:
The number of beats produced per second is **3 Hz**.

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