A whistle giving out `450 H_(Z)` approaches a stationary observer at a speed of `33 m//s`. The frequency heard the observer (in `H_(Z)`) is (speed of sound `= 330 m//s`)

Options

A. 409
B. 429
C. 517
D. 500

Explanation

To find the frequency heard by the observer when a whistle is approaching, 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 whistle (source frequency, \( f \)) = 450 Hz
- Speed of sound in air (\( v \)) = 330 m/s
- Speed of the source (\( v_s \)) = 33 m/s

### Step 2: Write the formula for apparent frequency
When the source is moving towards a stationary observer, the formula for the apparent frequency (\( f' \)) is given by:

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

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

\[ f' = \frac{330 \, \text{m/s}}{330 \, \text{m/s} - 33 \, \text{m/s}} \times 450 \, \text{Hz} \]

### Step 4: Simplify the denominator
Calculate the denominator:

\[ 330 \, \text{m/s} - 33 \, \text{m/s} = 297 \, \text{m/s} \]

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

\[ f' = \frac{330}{297} \times 450 \]

### Step 6: Calculate the fraction
Now calculate the fraction:

\[ \frac{330}{297} = \frac{10}{9} \quad \text{(after simplifying)} \]

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

\[ f' = \frac{10}{9} \times 450 \]

### Step 8: Perform the multiplication
Calculating this gives:

\[ f' = 500 \, \text{Hz} \]

### Conclusion
The frequency heard by the observer is **500 Hz**.

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