A car moving at 35 m/s approaches a stationary whistle that emits a 220 Hz sound. The speed of sound is 343 m/s. What is the speed of the sound relative to the driver of the car?

Options

A. 300 m/s
B. 340 m/s
C. 378 m/s
D. 305 m/s

Answer

To solve the problem step by step, we will find the speed of sound relative to the driver of the car.

### Step 1: Identify the given values
- Speed of sound in air, \( V_w = 343 \, \text{m/s} \)
- Speed of the car, \( V_c = 35 \, \text{m/s} \)
- Frequency of the sound emitted by the whistle, \( f = 220 \, \text{Hz} \) (not needed for this calculation)

### Step 2: Determine the direction of motion
The car is moving towards the stationary whistle. Therefore, we will consider the speed of sound as positive in the direction of the car's motion.

### Step 3: Calculate the speed of sound relative to the driver of the car
To find the speed of sound relative to the driver of the car, we will use the formula:
\[ V_{relative} = V_w - V_c \]
Where:
- \( V_{relative} \) is the speed of sound relative to the driver of the car.
- \( V_w \) is the speed of sound in air (343 m/s).
- \( V_c \) is the speed of the car (35 m/s).

### Step 4: Substitute the values into the formula
Substituting the known values:
\[ V_{relative} = 343 \, \text{m/s} - 35 \, \text{m/s} \]

### Step 5: Perform the calculation
\[ V_{relative} = 343 - 35 = 308 \, \text{m/s} \]

### Conclusion
The speed of sound relative to the driver of the car is \( 308 \, \text{m/s} \).

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