The frequency of a car horm is 400 Hz. If the horn is honked as the car moves with a speed `u_S=34(m)/(s)` through still air towards a stationary receiver, the wavelength of the sound passing the receiver is [velocity of sound is `340(m)/(s)`]

Options

A. 0.765 m
B. 0.850 m
C. 0.935 m
D. 0.425 m

Explanation

To find the wavelength of the sound passing the receiver when the car horn is honked, we can use the formula for the wavelength of sound emitted by a moving source towards a stationary observer. The formula is:

\[ \lambda = \frac{V - V_s}{f_s} \]

Where:
- \(\lambda\) = wavelength
- \(V\) = velocity of sound in air
- \(V_s\) = velocity of the source (the car)
- \(f_s\) = frequency of the source (the horn)

### Step 1: Identify the given values
- Frequency of the car horn, \(f_s = 400 \, \text{Hz}\)
- Velocity of sound, \(V = 340 \, \text{m/s}\)
- Velocity of the car (source), \(V_s = 34 \, \text{m/s}\)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the wavelength formula:

\[ \lambda = \frac{340 \, \text{m/s} - 34 \, \text{m/s}}{400 \, \text{Hz}} \]

### Step 3: Calculate the numerator
Calculate \(340 \, \text{m/s} - 34 \, \text{m/s}\):

\[ 340 - 34 = 306 \, \text{m/s} \]

### Step 4: Calculate the wavelength
Now, substitute the result back into the equation:

\[ \lambda = \frac{306 \, \text{m/s}}{400 \, \text{Hz}} \]

### Step 5: Perform the division
Now, perform the division:

\[ \lambda = 0.765 \, \text{m} \]

### Conclusion
The wavelength of the sound passing the receiver is \(0.765 \, \text{m}\).