An observer moves towards a stationary source of sound with a speed `((1)/(5))`th of the speed of sound. The wavelength and frequency of the source emitted are `lamda` and f, respectively. The apparent frequency and wavelength recorded by the observer are, respectively.

Options

A. `1.2f` and `lamda`
B. `f` and `1.2lamda`
C. `0.8` and `0.8lamda`
D. `1.2f` and `1.2lamda`

Explanation

To solve the problem, we need to find the apparent frequency and wavelength recorded by an observer moving towards a stationary sound source. Let's break it down step by step.

### Step 1: Understand the given information
- The speed of the observer (v_o) is given as \( \frac{1}{5} \) of the speed of sound (v).
- The original frequency of the source (f) and the wavelength (λ) are also given.

### Step 2: Use the Doppler Effect formula
The formula for the apparent frequency (f') when the observer is moving towards a stationary source is given by:

\[ f' = f \left( \frac{v + v_o}{v} \right) \]

### Step 3: Substitute the values
Since the observer is moving towards the source, we will use a positive sign for \( v_o \):

\[ f' = f \left( \frac{v + \frac{1}{5}v}{v} \right) \]

### Step 4: Simplify the equation
Now, we can simplify the expression:

\[ f' = f \left( \frac{v + \frac{1}{5}v}{v} \right) = f \left( \frac{1 + \frac{1}{5}}{1} \right) = f \left( \frac{6}{5} \right) \]

Thus, we have:

\[ f' = 1.2f \]

### Step 5: Determine the apparent wavelength
The wavelength (λ') observed by the observer can be calculated using the relationship between speed, frequency, and wavelength:

\[ \lambda' = \frac{v}{f'} \]

### Step 6: Substitute the values for wavelength
Substituting \( f' \):

\[ \lambda' = \frac{v}{1.2f} \]

### Step 7: Relate the original wavelength to the frequency
Since the original wavelength (λ) is given by:

\[ \lambda = \frac{v}{f} \]

We can express \( \lambda' \) in terms of λ:

\[ \lambda' = \frac{v}{1.2f} = \frac{1}{1.2} \cdot \frac{v}{f} = \frac{\lambda}{1.2} \]

### Final Results
Thus, the apparent frequency and wavelength recorded by the observer are:
- Apparent frequency: \( f' = 1.2f \)
- Apparent wavelength: \( \lambda' = \frac{\lambda}{1.2} \)