Step 1: Understanding the Concept:
The Doppler Effect describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.
In acoustic physics, when a sound source moves towards a stationary observer, the sound waves emitted by the source are compressed in the direction of motion.
Because the waves are closer together, the observer perceives more wave crests per unit of time, which corresponds to a higher frequency (pitch).
Conversely, if the source moves away, the waves are stretched, and the frequency appears lower.
Key Formula or Approach:
The master formula for the apparent frequency \(f'\) is:
\[ f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right) \]
Where:
\(f\) = actual frequency emitted by the source.
\(v\) = speed of sound in the medium.
\(v_o\) = speed of the observer.
\(v_s\) = speed of the source.
For a source approaching a stationary observer (\(v_o = 0\)), the denominator must be smaller than the numerator to reflect an increase in frequency.
Simplified formula: \(f' = f \left( \frac{v}{v - v_s} \right)\).
Step 2: Detailed Explanation:
Let's plug in the given values:
Original Frequency, \(f = 340\) Hz.
Speed of sound, \(v = 340\) m/s.
Speed of source, \(v_s = 10\) m/s.
Velocity of observer, \(v_o = 0\) m/s.
Substituting these values into the specialized Doppler equation:
\[ f' = 340 \left( \frac{340}{340 - 10} \right) \]
Calculate the value inside the bracket first:
\[ \text{Denominator} = 340 - 10 = 330 \]
\[ f' = 340 \times \left( \frac{340}{330} \right) \]
We can simplify the fraction by dividing both parts by 10:
\[ f' = 340 \times \frac{34}{33} \]
Performing the multiplication:
\[ f' = \frac{11560}{33} \]
Carrying out the division:
\[ f' \approx 350.303 \dots \]
Rounding to the nearest whole number to match the provided multiple-choice options, we get 350 Hz.
Step 3: Final Answer:
The apparent frequency is calculated as 350 Hz, which corresponds to option (A).