THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Open and closed pipes
A pipe open at both ends
A uniform pipe 0.85 m long is open at both ends.
Find its fundamental resonance frequency.
Organize the givens & assumptions
- L = 0.85 m
- v = 340 m/s
Uniform pipe open at both ends; sound speed 340 m/s; neglect end corrections.
Study with a tutor prompt
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Problem: A pipe open at both ends
A uniform pipe 0.85 m long is open at both ends.
Question: Find its fundamental resonance frequency.
Givens:
- L = 0.85 m
- v = 340 m/s
Assumptions: Uniform pipe open at both ends; sound speed 340 m/s; neglect end corrections.
Choices (LaTeX):
A. 340\ \mathrm{Hz}
B. 200\ \mathrm{Hz}
C. 100\ \mathrm{Hz}
D. 400\ \mathrm{Hz}
Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.
Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
The fundamental has displacement antinodes at both ends with half a wavelength inside the pipe.
Choose a physical relation
Open ends are displacement antinodes; the shortest standing-wave pattern between them spans half a wavelength.
Isolate what is asked
The fundamental has displacement antinodes at both ends with half a wavelength inside the pipe.
Why is this step valid?
Use wavelength twice the pipe length, then divide sound speed by that wavelength.
Substitute and interpret
Fundamental frequency is 200 Hz; the two open ends distinguish it from a quarter-wave pipe.
The inferred wavelength fits the correct end conditions.
TRY THE IDEA AGAIN
Close one end of this same pipe. What is the new ideal fundamental frequency?
YOUR LEARNING NOTE
How does this idea feel now?
Confidence is a reflection, not proof of mastery.
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