Step 1: Understanding the Concept:
The Doppler effect describes the change in frequency (and wavelength) of a wave in relation to an observer who is moving relative to the wave source.
When a source and an observer move towards each other, the waves are compressed, leading to a higher perceived frequency.
Step 2: Key Formula or Approach:
The apparent frequency $f'$ heard by the observer is given by:
\[ f' = f \left( \frac{v + v_o}{v - v_s} \right) \]
where $v$ is the speed of sound, $v_o$ is the speed of the observer (positive if moving towards the source), and $v_s$ is the speed of the source (positive if moving towards the observer).
The apparent wavelength $\lambda'$ is determined by the source's motion relative to the medium:
\[ \lambda' = \frac{v - v_s}{f} \]
Step 3: Detailed Explanation:
Both the source and the observer are moving towards each other.
Since the source is moving towards the observer, the wave fronts get bunched up in front of the source. This means the apparent wavelength $\lambda'$ decreases (it becomes lower than the actual wavelength $\lambda = v/f$).
Since the observer is also moving towards the source, they encounter these compressed wave fronts at a faster rate.
Looking at the frequency formula, the numerator $(v + v_o)$ is larger than $v$, and the denominator $(v - v_s)$ is smaller than $v$. Both of these effects cause the fraction to be greater than 1.
Therefore, the apparent frequency $f'$ is greater than the actual frequency $f$ (high frequency).
In conclusion, the observer hears a higher frequency and the sound has a lower wavelength.
Step 4: Final Answer:
The observer will hear high frequency, low wavelength.