A sound spurce is moving towards a stationary observer with 1/10 of the speed of sound. The ratio of apparent to real frequency is

Options

A. `10//9`
B. `11//10`
C. `(11//10)^(2)`
D. `(9//10)^(2)`

Answer

To solve the problem of finding the ratio of apparent frequency to real frequency when a sound source is moving towards a stationary observer at 1/10 of the speed of sound, we can follow these steps:

### Step 1: Understand the Doppler Effect
The Doppler Effect describes how the frequency of a wave changes for an observer moving relative to the source of the wave. When the source is moving towards the observer, the observed frequency (apparent frequency) increases.

### Step 2: Define Variables
Let:
- \( V \) = speed of sound
- \( V_s \) = speed of the source
- \( N_0 \) = real frequency (frequency emitted by the source)
- \( N' \) = apparent frequency (frequency observed)

Given that the source is moving towards the observer at \( V_s = \frac{1}{10} V \).

### Step 3: Use the Doppler Effect Formula
The formula for the apparent frequency when the source is moving towards a stationary observer is given by:

\[ N' = N_0 \frac{V}{V - V_s} \]

### Step 4: Substitute the Values
Substituting \( V_s = \frac{1}{10} V \) into the formula:

\[ N' = N_0 \frac{V}{V - \frac{1}{10} V} \]

### Step 5: Simplify the Expression
Now simplify the denominator:

\[ V - \frac{1}{10} V = \frac{10}{10} V - \frac{1}{10} V = \frac{9}{10} V \]

Thus, the formula for the apparent frequency becomes:

\[ N' = N_0 \frac{V}{\frac{9}{10} V} = N_0 \frac{10}{9} \]

### Step 6: Find the Ratio of Apparent to Real Frequency
The ratio of apparent frequency to real frequency is:

\[ \frac{N'}{N_0} = \frac{10}{9} \]

### Conclusion
The ratio of the apparent frequency to the real frequency when the sound source is moving towards the observer at 1/10 of the speed of sound is:

\[ \frac{N'}{N_0} = \frac{10}{9} \]