Questions: Closed Pipes Sound A well acts as a closed pipe. When wind blows across the top, it creates a fundamental frequency of 30.6 Hz. How deep is the well? (Speed of sound = 343 m/s) (Unit = m)

Closed Pipes
Sound

A well acts as a closed pipe. When
wind blows across the top, it
creates a fundamental frequency of
30.6 Hz. How deep is the well?

(Speed of sound = 343 m/s)
(Unit = m)

Transcript text: Closed Pipes Sound A well acts as a closed pipe. When wind blows across the top, it creates a fundamental frequency of 30.6 Hz. How deep is the well? (Speed of sound = 343 m/s) (Unit = m)

Solution

Solution Steps

Step 1: Understanding the Problem

We need to determine the depth of a well that acts as a closed pipe, given the fundamental frequency and the speed of sound.

Step 2: Formula for Fundamental Frequency in a Closed Pipe

The fundamental frequency \( f \) of a closed pipe is given by: \[ f = \frac{v}{4L} \] where:

\( f \) is the fundamental frequency,
\( v \) is the speed of sound,
\( L \) is the length (or depth) of the well.

Step 3: Solving for the Depth of the Well

Rearrange the formula to solve for \( L \): \[ L = \frac{v}{4f} \]

Step 4: Substituting the Given Values

Given:

\( f = 30.6 \) Hz,
\( v = 343 \) m/s,

Substitute these values into the formula: \[ L = \frac{343 \, \text{m/s}}{4 \times 30.6 \, \text{Hz}} \]

Step 5: Calculating the Depth

Perform the calculation: \[ L = \frac{343}{122.4} \approx 2.8021 \, \text{m} \]

Final Answer

\[ \boxed{L = 2.8021 \, \text{m}} \]

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