Step 1: Understanding the Concept:
This problem involves the Doppler Effect. When a source of sound moves toward a stationary observer, the wave fronts are "bunched up," causing the observer to perceive a higher frequency than the one actually emitted.
Step 2: Key Formula or Approach:
The apparent frequency \(f'\) is given by:
\[ f' = f \left( \frac{v}{v - v_s} \right) \]
Where \(v\) is the speed of sound and \(v_s\) is the velocity of the source.
Step 3: Detailed Explanation:
Given: \(f = 500\) Hz, \(v = 330\) m/s, and \(v_s = 30\) m/s.
Substituting the values into the formula:
\[ f' = 500 \left( \frac{330}{330 - 30} \right) \]
\[ f' = 500 \left( \frac{330}{300} \right) \]
\[ f' = 500 \times 1.1 = 550 \text{ Hz} \]
Step 4: Final Answer:
The frequency heard by the observer is 550 Hz.