What is the difference between the physical length $L$ and the acoustic length of the resonance tube?

The physical length $L$ is the measured distance from the tube top to the water. The acoustic length is $L + e$, where $e$ is the end correction representing the distance the antinode extends beyond the tube's open end.

How does the resonance pattern in a closed pipe differ from an open pipe?

A closed pipe has a node at one end and an antinode at the other, supporting only odd harmonics ($1/4 \lambda, 3/4 \lambda$). An open pipe has antinodes at both ends, supporting all harmonics ($1/2 \lambda, \lambda, 3/2 \lambda$).

Why is a graph of $L$ vs $1/f$ used instead of $L$ vs $f$?

The relationship $L = (v/4)(1/f) - e$ is linear with respect to $1/f$. Plotting $L$ vs $f$ would produce a hyperbola, which is much harder to analyze for gradient and intercept values.

What error occurs if the length $L$ is measured from the tuning fork to the water surface?

This introduces a systematic error because the air between the fork and the tube top is not part of the resonant column. Measurements must always start from the physical boundary of the tube's opening.

What is the consequence of mistaking the second resonance point for the fundamental resonance?

The second resonance occurs at $3/4 \lambda$. If you assume it is $1/4 \lambda$, your calculated wavelength will be three times too large, leading to a speed of sound that is three times the actual value.

How does parallax error affect the measurement of the air column length?

If the ruler is not viewed at eye level with the water meniscus, the recorded length $L$ will be consistently higher or lower than the true value, introducing random uncertainty into the data set.

Define 'End Correction' in the context of a resonance tube.

End correction is the small distance ($e$) beyond the physical end of a pipe where the pressure is not yet atmospheric, causing the displacement antinode to form slightly outside the tube.

What is a 'Node' in a standing wave?

A node is a point along a standing wave where the amplitude of vibration is always zero. In this practical, a displacement node forms at the water surface because the air molecules cannot move into the water.

What does the gradient of an $L$ vs $1/f$ graph represent?

The gradient $m$ represents $v/4$, where $v$ is the speed of sound. This is derived from the fundamental resonance condition $L + e = v/(4f)$.

Why does the sound become significantly louder at resonance?

At resonance, the reflected waves from the water surface interfere constructively with the incoming waves from the source, creating a standing wave with maximum pressure variations (loudness) at the antinode.

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5. Waves & Particle Nature of Light

Core Practical 6: Investigating the Speed of Sound

Summary

This practical utilizes the phenomenon of resonance in a closed-end air column to determine the speed of sound. By varying the length of the air column and identifying the points of maximum sound intensity for known frequencies, the relationship between frequency and wavelength is used to calculate the wave speed while accounting for systematic errors like end correction.

1. Definition & Core Concepts

Speed of Sound: The rate at which longitudinal pressure waves propagate through a medium, such as air, typically around $340$ m/s at room temperature.
Resonance: A condition where an external driving frequency matches the natural frequency of a system, leading to a significant increase in the amplitude of vibration.
Standing Waves in Pipes: In a tube closed at one end (e.g., by water), a standing wave forms with a displacement node at the closed end and a displacement antinode near the open end.
Fundamental Frequency: The lowest frequency at which resonance occurs, corresponding to the simplest standing wave pattern where the tube length is approximately one-quarter of the wavelength ( $\lambda/4$ ).

Diagram of a resonance tube partially submerged in water showing a standing wave with a node at the water surface and an antinode at the open end.

2. Underlying Principles

3. Methods & Techniques

Variable Length Setup: A hollow tube is placed inside a larger cylinder filled with water. Raising or lowering the tube changes the length of the air column above the water surface.
Frequency Selection: A series of tuning forks with known frequencies or a signal generator with a loudspeaker is used to provide the driving frequency.
Locating Resonance: The source is held over the open end while the tube is moved slowly. The point of resonance is identified by a distinct and sharp increase in the loudness of the sound.
Measurement Precision: The length $L$ from the top of the tube to the water surface is measured using a meter ruler. This process is repeated for multiple frequencies to generate a data set.

4. Key Distinctions

5. Data Analysis & Graphical Interpretation

6. Exam Strategy & Tips

7. Common Pitfalls & Misconceptions