AP Physics – Sound Waves and Doppler Effect

AP Physics – Sound Waves and Doppler Effect

AP Physics: Sound Waves & Doppler Effect – Exam-Ready Study Guide

What This Is

Sound waves are longitudinal mechanical waves that carry energy through a medium (like air, water, or solids) by compressing and rarefying particles. The Doppler Effect describes how the observed frequency of a wave changes when the source and observer are in relative motion. This topic is high-yield on the AP exam because it combines wave properties (frequency, wavelength, speed) with real-world applications (sirens, radar guns, astronomy). Example: When an ambulance speeds toward you, its siren sounds higher-pitched (higher frequency) due to the Doppler Effect—this is how astronomers detect the motion of stars and galaxies!

Key Terms & Concepts

• Sound wave: A longitudinal mechanical wave where particles oscillate parallel to the direction of wave travel. Requires a medium (cannot travel in a vacuum).
• Pitch: How high or low a sound is perceived; directly related to frequency (higher frequency = higher pitch).
• Loudness: Related to the amplitude of the sound wave (larger amplitude = louder sound).
• Speed of sound (v): Depends on the medium and temperature. In air at 20°C, v-343 m/s. Formula: v = f?
• v = speed of sound (m/s)
• f = frequency (Hz)
• ? = wavelength (m)
• Doppler Effect: The apparent shift in frequency of a wave due to relative motion between the source and observer.
• Moving source: Wavelengths compress (higher frequency) in front of the source and stretch (lower frequency) behind it.
• Moving observer: Observer encounters wavefronts faster (higher frequency) or slower (lower frequency).
• Doppler Effect formula (sound): f' = f (v ± v?) / (v-v?)
• f' = observed frequency (Hz)
• f = emitted frequency (Hz)
• v = speed of sound in medium (m/s)
• v? = speed of observer (m/s) (+ if moving toward source, – if moving away)
• v? = speed of source (m/s) (– if moving toward observer, + if moving away) Signs matter! The top sign is for the observer, the bottom for the source.
• Shock wave: Forms when a source moves faster than the speed of sound (e.g., a supersonic jet), creating a sonic boom (a loud, sudden pressure wave).
• Mach number: Ratio of an object’s speed to the speed of sound in the medium. Mach = v?bject / v?ound
• Beats: When two sound waves of slightly different frequencies interfere, producing a fluctuating loudness (beat frequency = |f? – f?|).
• Resonance: When a system (e.g., a guitar string, air column) vibrates at its natural frequency, amplifying the sound. Example: Blowing across a soda bottle to make a tone.

Step-by-Step: Solving Doppler Effect Problems

Follow these steps for any Doppler Effect question on the AP exam:

1. Identify the scenario:
2. Is the source moving, the observer moving, or both?

3. Are they moving toward or away from each other?

4. Assign signs to velocities:

5. Observer (v?): + if moving toward the source, – if moving away.
6. Source (v?): – if moving toward the observer, + if moving away.

7. Example: If a police car (source) is chasing you (observer), both are moving in the same direction. If the car is moving toward you, v? is –.

8. Plug into the Doppler formula: f' = f (v ± v?) / (v-v?)

9. Use the top sign for the observer, bottom sign for the source.

10. Check for supersonic speeds (if applicable):

11. If v? > v, the source is supersonic, and a shock wave forms (no Doppler shift in front of the source).

12. Solve for the unknown (f', v?, or v?).

13. If solving for f', ensure units are consistent (Hz).

14. If solving for v? or v?, rearrange the formula carefully.

15. Verify the answer makes sense:

16. If the source and observer are moving toward each other, f' should be higher than f.
17. If they’re moving apart, f' should be lower.

Common Mistakes

• Mistake: Mixing up the signs in the Doppler formula. Correction: Always use the top sign for the observer, bottom sign for the source. Draw a diagram if unsure!

• Mistake: Assuming the Doppler Effect only applies to sound. Correction: It applies to all waves (light, water, etc.), but the formula differs for light (relativistic Doppler Effect).

• Mistake: Forgetting that sound speed depends on the medium. Correction: In air, use 343 m/s at 20°C, but in water, sound travels ~1,500 m/s!

• Mistake: Confusing frequency (pitch) with amplitude (loudness). Correction: Frequency = pitch (Hz), amplitude = loudness (decibels, dB).

• Mistake: Ignoring units (e.g., using km/h instead of m/s). Correction: Always convert to m/s before plugging into formulas.

AP Exam Insights

1. Frequently tested scenarios:
2. Police sirens/ambulances (moving source, stationary observer).
3. Radar guns (moving observer, stationary source—reflected wave).

4. Astronomy (redshift/blueshift of light from stars).

5. Tricky distinctions:

6. Doppler Effect vs. resonance: Doppler is about relative motion, resonance is about natural frequency matching.

7. Speed of sound vs. speed of source: If v? > v, a shock wave forms (no Doppler shift in front).

8. FRQ types:

9. Calculating observed frequency (given speeds, solve for f').
10. Explaining real-world phenomena (e.g., why a siren’s pitch drops as it passes).

11. Graph interpretation (e.g., sketching wavefronts for a moving source).

12. Multiple-choice traps:

13. Sign errors (e.g., using + instead of – for a moving source).
14. Unit mismatches (e.g., km/h vs. m/s).
15. Assuming sound travels in a vacuum (it doesn’t!).

Quick Check Questions

1. Multiple Choice

A fire truck emits a siren at 800 Hz while moving toward a stationary observer at 30 m/s. If the speed of sound is 340 m/s, what frequency does the observer hear? (A) 730 Hz (B) 800 Hz (C) 875 Hz (D) 900 Hz

Answer: (C) 875 Hz Explanation: Use the Doppler formula with v? = 0 (observer stationary) and v? = –30 m/s (source moving toward observer). f' = 800 (340) / (340 – 30)-875 Hz.

2. Short FRQ

A bat emits a 50 kHz ultrasonic wave while flying toward a wall at 5 m/s. The wave reflects off the wall and returns to the bat. (a) What frequency does the wall “hear”? (b) What frequency does the bat hear upon reflection? Speed of sound = 340 m/s.

Answer: (a) 50.74 kHz Explanation: Wall is stationary (v? = 0), bat is moving toward it (v? = –5 m/s). f' = 50,000 (340) / (340 – 5)-50,740 Hz.

(b) 51.48 kHz Explanation: Now the wall is the source (emitting 50.74 kHz), and the bat is the moving observer (v? = +5 m/s). f'' = 50,740 (340 + 5) / 340-51,480 Hz.

Last-Minute Cram Sheet

1. Sound is a longitudinal wave—particles vibrate parallel to wave direction.
2. Speed of sound in air at 20°C = 343 m/s (faster in solids, slower in gases).
3. Doppler Effect formula: f' = f (v ± v?) / (v-v?) Signs matter!
4. Moving toward = higher frequency (compressed waves).
5. Moving away = lower frequency (stretched waves).
6. Sonic boom occurs when v? > v (source faster than sound).
7. Mach number = v?bject / v?ound (e.g., Mach 2 = twice the speed of sound).
8. Beats = |f? – f?| (used to tune instruments).
9. Resonance = natural frequency matching (e.g., breaking a glass with sound).
10. Sound cannot travel in a vacuum (needs a medium!).