Step 1: Understanding the Concept:
This question deals with the Doppler effect for sound.
When there is relative motion between a source of sound and an observer, the frequency heard by the observer differs from the actual frequency emitted by the source.
Step 2: Key Formula or Approach:
The general formula for apparent frequency is \( f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right) \), where \( v \) is the speed of sound, \( v_o \) is the observer's speed, and \( v_s \) is the source's speed.
The apparent wavelength in the medium is \( \lambda' = \frac{v - v_s}{f} \) when the source moves towards the observer.
Step 3: Detailed Explanation:
Here, the observer is stationary, so \( v_o = 0 \).
The source is moving towards the observer with velocity \( v_s \).
The apparent frequency formula becomes \( f' = f \left( \frac{v}{v - v_s} \right) \).
Since the denominator \( (v - v_s) \) is less than the numerator \( v \), the fraction is greater than 1.
Therefore, \( f'>f \), which means the apparent frequency increases.
Now let's consider the wavelength.
Wavelength is the distance between consecutive compressions in the medium.
Since the source is moving in the direction of wave propagation, it "catches up" to the waves it just emitted.
This compresses the waves in front of it.
The apparent wavelength is the distance the wave travels in one period minus the distance the source travels in that period.
\( \lambda' = \lambda - \Delta\lambda = \frac{v}{f} - \frac{v_s}{f} = \frac{v - v_s}{f} \).
Since \( v - v_s<v \), it follows that \( \lambda'<\lambda \).
Thus, the apparent wavelength decreases.
Step 4: Final Answer:
The apparent frequency increases while the wavelength decreases.