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 solve the problem of finding the frequency heard by a stationary observer when a whistle approaches at a certain speed, 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 whistle (f) = 450 Hz
- Speed of sound (Vs) = 330 m/s
- Speed of the whistle (Vw) = 33 m/s

### Step 2: Understand the Doppler effect formula
When a source of sound is moving towards a stationary observer, the apparent frequency (f') can be calculated using the formula:
\[ f' = f \times \frac{V_s}{V_s - V_w} \]
where:
- \( f' \) = apparent frequency heard by the observer
- \( f \) = actual frequency of the source
- \( V_s \) = speed of sound in the medium
- \( V_w \) = speed of the source of sound

### Step 3: Substitute the values into the formula
Now, we can substitute the known values into the formula:
\[ f' = 450 \times \frac{330}{330 - 33} \]

### Step 4: Calculate the denominator
Calculate the denominator:
\[ 330 - 33 = 297 \]

### Step 5: Substitute the denominator back into the formula
Now substitute this value back into the equation:
\[ f' = 450 \times \frac{330}{297} \]

### Step 6: Calculate the fraction
Now calculate the fraction:
\[ \frac{330}{297} \approx 1.11 \]

### Step 7: Calculate the apparent frequency
Now multiply this by the actual frequency:
\[ f' \approx 450 \times 1.11 \approx 500 \text{ Hz} \]

### Final Answer
The frequency heard by the observer is approximately **500 Hz**.

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