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. 550 Hz
B. 458.3 Hz
C. 530 Hz
D. 545.5 Hz

Answer

To find the frequency heard by the observer when a source of sound is moving towards them, we can use the Doppler effect formula for sound. Here’s how to solve the problem step by step:

### Step 1: Identify the given values
- Frequency of the source (f₀) = 500 Hz
- Velocity of the source (vₛ) = 30 m/s (moving towards the observer)
- Velocity of sound in air (v) = 330 m/s
- Velocity of the observer (vₒ) = 0 m/s (the observer is stationary)

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

\[ f = f₀ \left( \frac{v + vₒ}{v - vₛ} \right) \]

### Step 3: Substitute the known values into the formula
Since the observer is stationary, we can substitute vₒ = 0 into the formula:

\[ f = 500 \left( \frac{330 + 0}{330 - 30} \right) \]

### Step 4: Simplify the equation
Now, simplify the expression:

\[ f = 500 \left( \frac{330}{300} \right) \]

### Step 5: Calculate the apparent frequency
Now, we can calculate the value:

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

Calculating the fraction:

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

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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