a bus is moving with a velocity 4 m/s towards a wall, the driver sounds a horn of frequency 173 Hz . if the speed of sound in air is 350 m/s. the number of beat heard per second by a passanger on the bus will be

Options

A. one
B. two
C. three
D. four

Answer

To solve the problem, we need to determine the number of beats heard per second by a passenger on the bus when the bus is moving towards a wall and the driver sounds a horn. Here’s a step-by-step solution:

### Step 1: Identify the given data
- Velocity of the bus (v) = 4 m/s
- Frequency of the horn (f) = 173 Hz
- Speed of sound in air (v_s) = 350 m/s

### Step 2: Calculate the frequency of the sound heard by the passenger on the bus
Since the bus is moving towards the wall, we need to calculate the frequency of the sound that reflects off the wall and returns to the bus. The formula for the apparent frequency (f') when the source is moving towards a stationary observer is given by:

\[ f' = f \left( \frac{v_s + v}{v_s - v} \right) \]

Where:
- \( f' \) = apparent frequency
- \( f \) = actual frequency
- \( v_s \) = speed of sound
- \( v \) = speed of the source (bus)

### Step 3: Substitute the values into the formula
Substituting the values we have:

\[ f' = 173 \left( \frac{350 + 4}{350 - 4} \right) \]

### Step 4: Simplify the expression
Calculating the numerator and denominator:

\[ f' = 173 \left( \frac{354}{346} \right) \]

Now, calculate \( \frac{354}{346} \):

\[ \frac{354}{346} \approx 1.0231 \]

Now, substitute this back into the equation for \( f' \):

\[ f' \approx 173 \times 1.0231 \approx 176.46 \text{ Hz} \]

### Step 5: Calculate the number of beats per second
The number of beats per second (B) is given by the absolute difference between the apparent frequency and the actual frequency:

\[ B = |f' - f| \]

Substituting the values we found:

\[ B = |176.46 - 173| \approx 3.46 \text{ Hz} \]

### Step 6: Round to the nearest whole number
Since the number of beats is usually expressed as a whole number, we round 3.46 to 4 beats per second.

### Final Answer
The number of beats heard per second by a passenger on the bus is approximately **4 beats per second**.

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