Sound waves of frequency `600 H_(Z)` fall normally on perfectly reflecting wall. The distance from the wall at which the air particles have the maximum amplitude of vibration is (speed of sound in air = `330 m//s`)

Options

A. `(a)13.75 cm`
B. `(b)40. 25 cm`
C. `(c)70.5 cm`
D. `(d)60.75 cm`

Explanation

To solve the problem of finding the distance from the wall at which the air particles have the maximum amplitude of vibration when sound waves of frequency 600 Hz fall normally on a perfectly reflecting wall, we can follow these steps:

### Step 1: Understand the Concept of Antinodes
The maximum amplitude of vibration occurs at points called antinodes. For a wave reflecting off a wall, the first antinode is located at a distance of \( \frac{\lambda}{4} \) from the wall.

### Step 2: Calculate the Wavelength (\( \lambda \))
The wavelength of a sound wave can be calculated using the formula:
\[ \lambda = \frac{v}{f} \]
where:
- \( v \) is the speed of sound in air (given as 330 m/s),
- \( f \) is the frequency of the sound wave (given as 600 Hz).

Substituting the values:
\[ \lambda = \frac{330 \, \text{m/s}}{600 \, \text{Hz}} = 0.55 \, \text{m} \]

### Step 3: Convert Wavelength to Centimeters
Since the options are in centimeters, we convert the wavelength from meters to centimeters:
\[ \lambda = 0.55 \, \text{m} \times 100 \, \text{cm/m} = 55 \, \text{cm} \]

### Step 4: Calculate the Distance to the First Antinode
The distance from the wall to the first antinode is given by:
\[ \text{Distance to first antinode} = \frac{\lambda}{4} \]
Substituting the value of \( \lambda \):
\[ \text{Distance} = \frac{55 \, \text{cm}}{4} = 13.75 \, \text{cm} \]

### Step 5: Conclusion
Thus, the distance from the wall at which the air particles have the maximum amplitude of vibration is:
\[ \text{Distance} = 13.75 \, \text{cm} \]

### Final Answer
The required answer is \( 13.75 \, \text{cm} \).

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