A source having frequency of 240 Hz is moving towards an observer with a speed of 20 m/sec. When the observer is moving towards the source with a velocity of 20 m/sec, then apparent frequency heard by the observer, if velocity is 330 m/sec will be

Options

A. 245 Hz
B. 268 Hz
C. 271 Hz
D. 260 Hz

Explanation

To solve the problem of finding the apparent frequency heard by the observer when both the source and the observer are moving towards each other, we can use the Doppler effect formula for sound. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Frequency of the source (f) = 240 Hz
- Speed of sound in air (v) = 330 m/s
- Speed of the source (vs) = 20 m/s (moving towards the observer)
- Speed of the observer (vo) = 20 m/s (moving towards the source)

### Step 2: Write down the formula for apparent frequency
The formula for the apparent frequency (f') when both the source and the observer are moving towards each other is given by:

\[ f' = f \times \frac{v + v_o}{v - v_s} \]

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

### Step 3: Substitute the values into the formula
Now, substitute the known values into the formula:

\[ f' = 240 \times \frac{330 + 20}{330 - 20} \]

### Step 4: Simplify the equation
Calculate the numerator and the denominator:

- Numerator: \( 330 + 20 = 350 \)
- Denominator: \( 330 - 20 = 310 \)

Now, substitute these values back into the equation:

\[ f' = 240 \times \frac{350}{310} \]

### Step 5: Calculate the apparent frequency
Now we can calculate \( f' \):

\[ f' = 240 \times \frac{350}{310} \approx 240 \times 1.1290 \approx 271 \text{ Hz} \]

### Step 6: Conclusion
The apparent frequency heard by the observer is approximately 271 Hz.

### Final Answer
The correct option is **C) 271 Hz**.

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