A wave source of frequency v and an observer are located a fixed distance apart. Both the source and observer are stationary. However, the propagation medium (through which the waves travel at speed v) is moving at a uniform velocity `v_(m)` in an arbitrary direction. If v' is the frequency received by the observer then :

Options

A. `v' ne v`
B. `v' = v` as the transit time from source to observer is the same for all wave fronts
C. `v' lt v` as the transit time from source to observer is the same for all wave fronts
D. Data Insufficient

Explanation

To solve the problem, we need to analyze the situation using the principles of wave propagation and the Doppler effect. Here’s a step-by-step solution:

### Step 1: Understand the setup
We have a wave source that emits waves at a frequency \( f_0 \) (given as \( v \)) and an observer. Both the source and observer are stationary, meaning their velocities \( v_s \) (source) and \( v_o \) (observer) are both zero. The medium through which the waves propagate is moving with a uniform velocity \( v_m \).

**Hint:** Identify the key elements in the problem: source frequency, observer position, and medium velocity.

### Step 2: Apply the Doppler Effect
The Doppler effect formula for sound waves when both the source and observer are stationary is given by:

\[ f' = f_0 \cdot \frac{v + v_o}{v + v_s} \]

Where:
- \( f' \) is the frequency received by the observer.
- \( f_0 \) is the frequency of the source.
- \( v \) is the speed of sound in the medium.
- \( v_o \) is the velocity of the observer (0 in this case).
- \( v_s \) is the velocity of the source (0 in this case).

**Hint:** Recall the Doppler effect formula and note that both \( v_o \) and \( v_s \) are zero.

### Step 3: Substitute the values
Since both the observer and source are stationary, we substitute \( v_o = 0 \) and \( v_s = 0 \) into the Doppler effect equation:

\[ f' = f_0 \cdot \frac{v + 0}{v + 0} = f_0 \cdot \frac{v}{v} = f_0 \]

**Hint:** Simplify the equation by substituting the values of \( v_o \) and \( v_s \).

### Step 4: Relate \( f_0 \) to the given frequency
From the problem, we know \( f_0 = v \). Therefore, we can write:

\[ f' = v \]

**Hint:** Recognize that the frequency of the source is given as \( v \).

### Step 5: Conclusion
Thus, the frequency received by the observer \( f' \) is equal to the frequency of the source \( f_0 \):

\[ f' = v \]

This means that the frequency received by the observer is the same as the frequency emitted by the source.

**Final Answer:** The frequency received by the observer \( f' \) is equal to the frequency of the source \( v \).