AP Physics Questions on Sound Production in Musical Instruments

📚 Quick Study Guide

• 📏 Wavelength and Frequency: The wavelength ($\lambda$) and frequency ($f$) of a sound wave are related by the speed of sound ($v$): $v = f\lambda$.
• 🎻 Stringed Instruments: The fundamental frequency of a vibrating string is given by $f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$, where $L$ is the length of the string, $T$ is the tension, and $\mu$ is the linear mass density.
• 🎺 Open Pipes: Open pipes (both ends open) have harmonic frequencies given by $f_n = n\frac{v}{2L}$, where $n = 1, 2, 3,...$
• 🎷 Closed Pipes: Closed pipes (one end closed) have harmonic frequencies given by $f_n = n\frac{v}{4L}$, where $n = 1, 3, 5,...$ (only odd harmonics).
• 🔊 Resonance: Resonance occurs when the frequency of a driving force matches a natural frequency of the system, leading to a large amplitude vibration.
• 🌡️ Speed of Sound: The speed of sound in air depends on temperature: $v = 331 + 0.6T$, where $T$ is the temperature in Celsius.
• 🎵 Harmonics: Harmonics are integer multiples of the fundamental frequency and determine the timbre (tone color) of the sound.

Practice Quiz

1. A guitar string of length 0.75 m has a fundamental frequency of 440 Hz. What is the speed of the wave on the string?
   1. 165 m/s
   2. 330 m/s
   3. 660 m/s
   4. 880 m/s
2. An open pipe has a length of 1.5 m. If the speed of sound is 343 m/s, what is the frequency of the second harmonic?
   1. 57.2 Hz
   2. 114.3 Hz
   3. 228.7 Hz
   4. 457.3 Hz
3. A closed pipe has a length of 0.8 m. If the speed of sound is 340 m/s, what is the frequency of the fundamental mode?
   1. 106.25 Hz
   2. 212.5 Hz
   3. 425 Hz
   4. 850 Hz
4. If the tension in a string is quadrupled, what happens to the fundamental frequency?
   1. It is halved.
   2. It remains the same.
   3. It doubles.
   4. It quadruples.
5. What happens to the speed of sound in air as the temperature increases?
   1. It decreases.
   2. It remains the same.
   3. It increases.
   4. It oscillates.
6. Which of the following is NOT a characteristic of sound waves?
   1. Amplitude
   2. Frequency
   3. Wavelength
   4. Polarization
7. A flute can be modeled as an open pipe. If a flute plays a note at 262 Hz, what is the frequency of the next highest harmonic it can produce?
   1. 131 Hz
   2. 393 Hz
   3. 524 Hz
   4. 786 Hz