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Question

A sound source is moving towards a stationary observer. The observer will hear a frequency that is:

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Doppler Effect
 **Related Topics**: Wave motion, sound waves
 **Prerequisites**: Understanding of wave frequency and relative motion.
## SOLUTION PATHWAY
**Given Information**:
  A sound source is moving towards a stationary observer.
  
**Method & Steps**:
 1. Understanding the Doppler Effect: The Doppler effect describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave.  When a source of sound moves towards a stationary observer, the sound waves are compressed, resulting in a higher frequency perceived by the observer.
  Reasoning: The closer the sound waves get to the observer, the more frequently they arrive.
  Formula/Rule: The formula for the Doppler effect when the source is moving towards a stationary observer is:
$f_o = f_s \frac{v}{v - v_s}$ 
where:
$f_o$ is the observed frequency
$f_s$ is the source frequency
$v$ is the speed of sound
$v_s$ is the speed of the source
Since $v_s$ is positive and subtracted from $v$ in the denominator, $f_o$ will be greater than $f_s$.
 2. Applying the formula: The formula shows that when the source moves towards the observer ($v_s$ is positive), the observed frequency ($f_o$) is higher than the source frequency ($f_s$).
  Working:  As $v_s$ increases (source moving faster), the denominator decreases, thus increasing $f_o$.
  Key Point: The Doppler effect applies to all types of waves, not just sound waves.
 3. Final step: The observer will hear a frequency higher than the emitted frequency.
  Result: Higher than the emitted frequency
  Verification: The derived formula and the conceptual understanding of wave compression both confirm the result.
 ## OPTION ANALYSIS
A ✓: Higher than the emitted frequency. This is correct due to the compression of sound waves as the source approaches the observer.
B :x: Lower than the emitted frequency. This would be the case if the source were moving away from the observer.
C :x: The same as the emitted frequency. This is only true if there is no relative motion between the source and the observer.
D :x: Zero.  The frequency would only be zero if the source were not producing any sound.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing the direction of motion: Remember that the source moving towards the observer leads to a higher frequency, and moving away leads to a lower frequency.
  2.Incorrectly applying the formula: Ensure you use the correct formula based on whether the source or observer is moving and in which direction.
 **Quick Tips**:
  1.Visualize the sound waves: Imagine the waves being compressed as the source approaches.
  2.Remember the mnemonic: Towards - higher, Away - lower

ABDUL JILANI BASHA · Answer

The correct Option is "Higher than the emitted frequency"

ABDUL JILANI BASHA · Answer

Lower than the emitted frequency

ABDUL JILANI BASHA · Answer

The same as the emitted frequency

ABDUL JILANI BASHA · Answer

Zero

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