Speed of Sound Lab

Speed of Sound Lab: Closed Pipe Resonance

Verified Content Badge

How fast does sound travel? This deceptively simple question has fascinated scientists for centuries. One elegant method for measuring the speed of sound uses resonance in air columns—when a tuning fork of known frequency causes standing waves in a tube of adjustable length, we can determine the speed of sound from the resonant conditions.

This lab simulation recreates the classic resonance tube experiment, allowing you to find resonance points and calculate the speed of sound in air.

The Physics of Closed Pipe Resonance

Standing Waves in Tubes

When sound waves travel down a tube, they reflect off the ends. In a closed pipe (one end closed, one open), the boundary conditions create standing wave patterns [1]:

• Closed end: Must be a displacement node (air cannot move into the wall)
• Open end: Must be a displacement antinode (air moves freely)

These constraints mean that only certain wavelengths "fit" in the tube—these are the resonant modes.

Resonance Conditions

For a closed pipe of length L, resonance occurs when [2]:

$L = n\frac{\lambda}{4} \quad (n = 1, 3, 5, 7...)$

Since λ = v/f, we can write:

$f_n = \frac{nv}{4L} \quad (n = 1, 3, 5, 7...)$

Note: Only odd harmonics are present in a closed pipe!

Determining Speed of Sound

Rearranging the resonance equation:

$v = \frac{4fL}{n}$

By measuring L at resonance (when sound is loudest) and knowing f from the tuning fork, we can calculate v.

Key Equations

Learning Objectives

After completing this lab, you should be able to:

1. Explain why closed pipes only produce odd harmonics
2. Locate resonance points by adjusting tube length
3. Calculate the speed of sound from resonance data
4. Identify nodes and antinodes in standing wave patterns
5. Describe how temperature affects the speed of sound
6. Compare closed and open pipe resonance conditions

Exploration Activities

Activity 1: Find the First Resonance

Objective: Locate the fundamental (n=1) resonance for a 256 Hz tuning fork.

Procedure:

1. Select the C4 (256 Hz) tuning fork
2. Click "Strike Fork" to start the sound
3. Slowly increase the tube length from 5 cm
4. Watch the amplitude indicator—it peaks at resonance
5. Record the resonant length L₁

Expected result: At 20°C, v ≈ 343 m/s, so L₁ = v/(4f) ≈ 33.5 cm

Activity 2: Find Multiple Harmonics

Objective: Verify the relationship between resonant lengths.

Procedure:

1. Keep f = 256 Hz
2. Find resonances for n = 1, 3, 5
3. Record L₁, L₃, L₅
4. Calculate L₃/L₁ and L₅/L₁

Expected result: L₃/L₁ ≈ 3 and L₅/L₁ ≈ 5

Activity 3: Effect of Frequency

Objective: Explore how frequency affects resonant length.

Procedure:

1. Find L₁ for frequencies 256, 384, and 512 Hz
2. Plot L₁ vs 1/f
3. Calculate the slope

Analysis: The slope equals v/4, allowing you to determine v without knowing any individual λ.

Activity 4: Temperature Dependence

Objective: Measure how temperature affects the speed of sound.

Procedure:

1. Set T = 0°C and find L₁ for 256 Hz
2. Repeat at T = 20°C and T = 40°C
3. Calculate v for each temperature
4. Compare with v = 331 + 0.6T

Real-World Applications

Reference Data: Speed of Sound

Data from CRC Handbook of Chemistry and Physics [3].

Challenge Questions

Level 1 (Basic):

1. A closed pipe resonates at its fundamental with L = 25 cm and f = 343 Hz. What is the speed of sound?

Level 2 (Intermediate): 2. At what length would the same pipe resonate at the third harmonic (n=3)?

Level 3 (Advanced): 3. An open pipe and closed pipe have the same fundamental frequency. How do their lengths compare?

Level 4 (Challenge): 4. A closed pipe at 20°C has L₁ = 33.0 cm for a 260 Hz fork. Calculate v and your percentage error from the expected value.

Level 5 (Extension): 5. Why is the speed of sound in helium (~1,007 m/s) much higher than in air? (Hint: consider molecular mass and v ∝ √(T/M))

Common Mistakes to Avoid

Frequently Asked Questions

Q: Why do closed pipes only have odd harmonics? A: The boundary conditions (node at closed end, antinode at open) require L = nλ/4 where n is odd. Even n would place either two nodes or two antinodes at the ends, violating the boundary conditions [1].

Q: What's the "end correction" mentioned in some textbooks? A: The antinode doesn't form exactly at the tube opening—it's slightly outside. The effective length is L + 0.6r (where r is the tube radius). For precise measurements, this correction should be applied [2].

Q: Why does temperature affect sound speed? A: Sound travels through molecular collisions. At higher temperatures, molecules move faster, transmitting vibrations more quickly. v ∝ √T (where T is in Kelvin) [4].

Q: How accurate is this method for measuring v? A: With careful measurements, you can achieve ±1-2% accuracy. Main error sources: imprecise resonance detection, temperature uncertainty, and end correction.

Q: Can I use any frequency tuning fork? A: Yes, but the resonant lengths must fit in your tube. Lower frequencies need longer tubes (L₁ ∝ 1/f).

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics, 10th Edition. Wiley. Chapter 17: Waves-II.

[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers, 10th Edition. Cengage Learning. Chapter 18: Superposition and Standing Waves.

[3] Haynes, W. M. (Ed.). (2016). CRC Handbook of Chemistry and Physics, 97th Edition. CRC Press.

[4] Knight, R. D. (2016). Physics for Scientists and Engineers: A Strategic Approach, 4th Edition. Pearson.

About the Data

Speed of sound values at standard conditions are from the CRC Handbook. The temperature relationship v = 331 + 0.6T is an approximation valid for typical atmospheric conditions.

Citation Guide

To cite this simulation in academic work:

Simulations4All. (2025). Speed of Sound Lab [Interactive simulation]. Simulations4All Educational Platform. Retrieved from https://simulations4all.com/simulations/speed-of-sound-lab

Verification Log