A soure of sound of frequency 165 Hz generates sound waves which get fully reflected from a wall . A person standing at the wall starts moving away from the wall. The minimum distance of the point from the wall at which the person hears maximum sound is (velcoity of sound = 330 `ms^(-1)`)

Options

A. 1m
B. 2 m
C. 1/2 m
D. 1/4 m

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript:

### Step 1: Understand the Problem
We have a source of sound generating waves at a frequency of 165 Hz, and these waves reflect off a wall. A person is moving away from the wall, and we need to find the minimum distance from the wall at which the person hears the maximum sound.

### Step 2: Identify Key Parameters
- Frequency of sound (ν) = 165 Hz
- Velocity of sound (v) = 330 m/s
- We need to find the wavelength (λ) of the sound waves.

### Step 3: Calculate the Wavelength
The wavelength (λ) can be calculated using the formula:
\[ \lambda = \frac{v}{\nu} \]
Substituting the known values:
\[ \lambda = \frac{330 \, \text{m/s}}{165 \, \text{Hz}} = 2 \, \text{m} \]

### Step 4: Determine Path Difference for Maximum Sound
For the person to hear maximum sound, the path difference (Δx) between the direct sound wave and the reflected sound wave must be equal to the wavelength (λ):
\[ \Delta x = \lambda \]
From the setup, the path difference when the person is at distance \(d\) from the wall is:
\[ \Delta x = 2d \]
Setting this equal to the wavelength:
\[ 2d = \lambda \]
Substituting the value of λ:
\[ 2d = 2 \, \text{m} \]

### Step 5: Solve for Distance \(d\)
Now, we can solve for \(d\):
\[ d = \frac{2 \, \text{m}}{2} = 1 \, \text{m} \]

### Conclusion
The minimum distance from the wall at which the person hears maximum sound is:
\[ \boxed{1 \, \text{m}} \]