📚 Topic Summary
In a tube, standing waves occur when a wave is confined and reflects back on itself, creating points of maximum displacement (antinodes) and zero displacement (nodes). Harmonics are integer multiples of the fundamental frequency ($f_1$), which is the lowest frequency at which a standing wave can form. Overtones are frequencies above the fundamental frequency. For a tube open at both ends, all harmonics are possible ($f_n = n \frac{v}{2L}$), where $n = 1, 2, 3,...$, $v$ is the speed of sound, and $L$ is the length of the tube. For a tube closed at one end, only odd harmonics are possible ($f_n = n \frac{v}{4L}$), where $n = 1, 3, 5,...$). This difference impacts the sound produced by instruments like flutes (open tubes) and clarinets (closed tubes).
🧪 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Harmonic |
A. The lowest resonant frequency of a vibrating object. |
| 2. Overtone |
B. A wave that appears to stand still, with nodes and antinodes. |
| 3. Fundamental Frequency |
C. A frequency higher than the fundamental frequency. |
| 4. Node |
D. An integer multiple of the fundamental frequency. |
| 5. Standing Wave |
E. A point along a standing wave where the amplitude is minimum. |
✍️ Part B: Fill in the Blanks
Standing waves in a tube are formed by the __________ of waves. The points of maximum displacement are called __________, while the points of zero displacement are called __________. The lowest frequency at which a standing wave can form is called the __________ __________. In a tube open at both ends, __________ harmonics are possible.
🤔 Part C: Critical Thinking
Imagine you have two tubes of the same length, one open at both ends and one closed at one end. How would the fundamental frequency and the resulting sound differ between the two tubes? Explain your reasoning using the formulas for the frequencies of standing waves in open and closed tubes.