Understanding the Concepts

* Closed Pipes: A pipe closed at one end has a fundamental frequency (first harmonic) where the closed end is a node (no displacement) and the open end is an antinode (maximum displacement).

* Harmonics: The harmonics of a closed pipe are odd multiples of the fundamental frequency.

* Wave Speed: The speed of a wave is related to its frequency (f) and wavelength (λ) by the equation: v = fλ

Solution

1. Determine the Harmonic: Since we're given a harmonic frequency, we need to figure out which harmonic it represents. For a closed pipe, the harmonics are:

* 1st harmonic: f₁

* 3rd harmonic: 3f₁

* 5th harmonic: 5f₁

* and so on...

2. Find the Fundamental Frequency: The given frequency (466.2 Hz) must be an odd multiple of the fundamental frequency (f₁). To find f₁, we need to figure out the appropriate multiple:

* If 466.2 Hz is the 1st harmonic (f₁), then f₁ = 466.2 Hz

* If 466.2 Hz is the 3rd harmonic (3f₁), then f₁ = 466.2 Hz / 3 ≈ 155.4 Hz

* And so on...

3. Calculate the Wavelength: The length of the pipe (L) is related to the wavelength (λ) of the fundamental frequency in a closed pipe by the following:

* L = λ/4

* Therefore, λ = 4L = 4 * 1.53 m = 6.12 m

4. Calculate the Wave Speed: Now, we can use the wave speed equation:

* v = fλ

* v = f₁ * λ

* v = 155.4 Hz * 6.12 m

* v ≈ 950.8 m/s

Answer: The speed of the wave in the pipe is approximately 950.8 m/s.