Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be _____ Hz. [Velocity of sound in air is 340 m/s.]

Answer

To solve the problem of the beat frequency heard by each driver of the two cars approaching each other, we will use the Doppler effect formula. Here’s a step-by-step solution:

### Step 1: Convert the speed of the cars from km/hr to m/s
The speed of the cars is given as 7.2 km/hr. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]
Calculating this:
\[ 7.2 \times \frac{5}{18} = 2 \text{ m/s} \]

### Step 2: Identify the parameters for the Doppler effect
In this scenario:
- \( f_0 = 676 \) Hz (the frequency of the horns)
- \( v = 340 \) m/s (the speed of sound in air)
- \( v_s = 2 \) m/s (the speed of the source, which is the car blowing the horn)
- \( v_o = 2 \) m/s (the speed of the observer, which is the other car)

### Step 3: Apply the Doppler effect formula
The formula for the observed frequency \( f \) when both the source and observer are moving towards each other is:
\[ f = f_0 \times \frac{v + v_o}{v - v_s} \]
Substituting the values we have:
\[ f = 676 \times \frac{340 + 2}{340 - 2} \]
This simplifies to:
\[ f = 676 \times \frac{342}{338} \]

### Step 4: Calculate the observed frequency
Now we compute the value:
\[ f = 676 \times 1.012 = 684 \text{ Hz (approximately)} \]

### Step 5: Calculate the beat frequency
The beat frequency \( f_b \) is the difference between the observed frequency \( f \) and the original frequency \( f_0 \):
\[ f_b = |f - f_0| = |684 - 676| = 8 \text{ Hz} \]

### Final Answer
The beat frequency heard by each driver will be **8 Hz**.

---