A source is moving towards an observer with a speed of 20 m / s and having frequency of 240 Hz . The observer is now moving towards the source with a speed of 20 m / s . Apparent frequency heard by observer, if velocity of sound is 340 m / s , is

Options

A. 268 Hz
B. 270 Hz
C. 360 Hz
D. 240 Hz

Explanation

To solve the problem of finding the apparent frequency heard by the observer, we can use the Doppler effect formula for sound. The formula for the apparent frequency \( f' \) when both the source and the observer are moving towards each other is given by:

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

Where:
- \( f' \) = apparent frequency
- \( f \) = actual frequency of the source (240 Hz)
- \( v \) = speed of sound in air (340 m/s)
- \( v_o \) = speed of the observer (20 m/s, positive since the observer is moving towards the source)
- \( v_s \) = speed of the source (20 m/s, positive since the source is moving towards the observer)

### Step 1: Identify the values
- Actual frequency \( f = 240 \) Hz
- Speed of sound \( v = 340 \) m/s
- Speed of the observer \( v_o = 20 \) m/s
- Speed of the source \( v_s = 20 \) m/s

### Step 2: Substitute the values into the formula
Substituting the known values into the Doppler effect formula:

\[ f' = 240 \cdot \frac{340 + 20}{340 - 20} \]

### Step 3: Simplify the equation
Calculating the numerator and denominator:

\[ f' = 240 \cdot \frac{360}{320} \]

### Step 4: Further simplify the fraction
Now, simplify \( \frac{360}{320} \):

\[ \frac{360}{320} = \frac{9}{8} \]

### Step 5: Calculate the apparent frequency
Now substitute back into the equation:

\[ f' = 240 \cdot \frac{9}{8} \]

Calculating this gives:

\[ f' = 240 \cdot 1.125 = 270 \text{ Hz} \]

### Final Answer
The apparent frequency heard by the observer is **270 Hz**.

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