A vehicle , with a horn of frequency `n` is moving with a velocity of `30 m//s` in a direction prependicular to the straight line joining the observer and the vehicle . The observer perceives the sound to have a grequency `(n + n_(1))` . If the sound velocity in air is `330 m//s` , then

Options

A. `n_(1) = 10 n`
B. `n_(1) = 0`
C. `n_(1) = 0.1 n`
D. `n_(1) = - 0.1 n`

Explanation

To solve the problem, we need to determine the change in frequency (n1) perceived by the observer when the vehicle is moving with a horn of frequency n. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Scenario
We have a vehicle emitting sound at a frequency \( n \) and moving with a velocity of \( 30 \, \text{m/s} \) perpendicular to the line joining the observer and the vehicle. The speed of sound in air is given as \( 330 \, \text{m/s} \).

### Step 2: Identify the Apparent Frequency Formula
The apparent frequency \( f' \) perceived by the observer can be calculated using the Doppler effect formula. However, since the source is moving perpendicular to the line of sight, the formula simplifies. The apparent frequency is given by:

\[ f' = f \cdot \frac{v}{v - v_s} \]

Where:
- \( f' \) is the apparent frequency.
- \( f \) is the original frequency (n).
- \( v \) is the speed of sound in air (330 m/s).
- \( v_s \) is the speed of the source (30 m/s).

### Step 3: Apply the Formula
Since the source is moving perpendicular to the observer, the effective frequency perceived by the observer does not change due to the Doppler effect in this specific case. Thus, we can consider:

\[ f' = f = n \]

### Step 4: Relate Apparent Frequency to the Given Condition
According to the problem, the observer perceives the sound to have a frequency \( f' = n + n_1 \). Since we established that \( f' = n \):

\[ n = n + n_1 \]

### Step 5: Solve for \( n_1 \)
Rearranging the equation gives:

\[ n - n = n_1 \]

This simplifies to:

\[ n_1 = 0 \]

### Conclusion
The value of \( n_1 \) is \( 0 \).

### Final Answer
Thus, the frequency perceived by the observer is the same as the emitted frequency, and \( n_1 = 0 \).

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