A source of sound of frequency 500 Hz is moving towards an observer with velocity 30 m/s . The speed of sound is 330 m/s . the frequency heard by the observer will be

Options

A. 500 Hz
B. 550 Hz
C. 355 Hz
D. 55.5 Hz

Answer

To find the frequency heard by the observer when a sound source is moving towards them, we can use the Doppler Effect formula. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Frequency of the source (f) = 500 Hz
- Velocity of the source (vs) = 30 m/s (moving towards the observer)
- Speed of sound (v) = 330 m/s

### Step 2: Write the formula for the apparent frequency
The formula for the apparent frequency (f') when the source is moving towards the observer is given by:

\[ f' = f \times \frac{v}{v - vs} \]

Where:
- \( f' \) = apparent frequency heard by the observer
- \( f \) = frequency of the source
- \( v \) = speed of sound
- \( vs \) = speed of the source

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

\[ f' = 500 \times \frac{330}{330 - 30} \]

### Step 4: Calculate the denominator
Calculate \( 330 - 30 \):

\[ 330 - 30 = 300 \]

### Step 5: Substitute back into the formula
Now substitute this back into the formula:

\[ f' = 500 \times \frac{330}{300} \]

### Step 6: Perform the division
Calculate \( \frac{330}{300} \):

\[ \frac{330}{300} = 1.1 \]

### Step 7: Calculate the apparent frequency
Now multiply by 500:

\[ f' = 500 \times 1.1 = 550 \text{ Hz} \]

### Final Answer
The frequency heard by the observer is **550 Hz**.

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