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**Problem 5:** Consider standing waves in a pipe of length \( L = 1.5 \, \text{m} \) containing a column of air. The speed of sound in the columns is \( v_s = 343 \, \text{m/s} \). Each of the standing wave images provided may represent a case for which one or both ends are open.

**Assignment Details**

**Part (a):** Select the image from the options provided showing the displacement of air particles for the third harmonic of a pipe with two open ends.
- Correct Answer: Image depicting a wave with three full oscillations.
- Feedback: Correct!

**Part (b):** Calculate the wavelength λ₃ in meters for the third harmonic in the pipe with two open ends.

**Part (c):** Calculate the frequency f₁ in Hz for the fundamental harmonic in the pipe with two open ends.

**Part (d):** Select the image from the options provided showing the displacement of air particles for the third mode of a pipe with one open end and one closed end (the third mode is the third possible excitation).
- Table for Correct Answer and Student Final Submission included, showing an image similar to Part (a) with feedback marked as "Correct!"

**Submission History:**
- All Date times are displayed in Central Standard Time. Red submission date times indicate late work.

| Date | Time | Answer (Image) | Hints | Feedback |
|----------------|--------|-----------------------|-------|----------|
| Nov 18, 2021 | 9:24 PM| Image with three waves | | Note: Feedback not accessed. |
| Nov 18, 2021 | 9:24 PM| Image with three waves | | |

**Part (e):** Calculate the frequency f₁ in Hz for the fundamental harmonic in the pipe with one open and one closed end.

**Part (f):** Select the image from the options provided showing the displacement of air particles for the third harmonic of a pipe with two closed ends.
- Correct Answer: Image depicting a wave with three full oscillations.
- Feedback: Correct!

**Part (g):** Calculate the frequency f₁ in Hz for the fundamental harmonic in the pipe with two closed ends.

**Part (h):** Choose the correct statement from the options below.

**Graph and Diagram Details:**
The images provided in Parts (a) and (f) display sinusoidal-like waveforms indicative of harmonic frequencies in a pipe, with three full oscillations within the given boundary conditions. These illustrate the theoretical displacement patterns of air particles corresponding to specific harmonics.

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