How does the 'end correction' affect the measurement of the air column length at resonance?

The end correction ($e$) means the antinode forms slightly outside the tube. Consequently, the measured length $L$ is slightly shorter than the actual wave component (e.g., $L < \lambda/4$), leading to an underestimation of wavelength if not corrected.

Why is the subtraction method ($L_2 - L_1$) preferred over using a single resonance length?

Subtracting $L_1$ from $L_2$ eliminates the end correction constant ($e$) from the calculation. Since $L_1 + e = \lambda/4$ and $L_2 + e = 3\lambda/4$, the difference $(L_2 - L_1)$ equals exactly $\lambda/2$, regardless of the value of $e$.

What boundary condition exists at the water surface in the resonance tube?

A displacement node exists at the water surface. This is because the water acts as a fixed boundary where the air molecules are restricted from longitudinal movement, resulting in zero displacement amplitude.

If the frequency of the tuning fork is doubled, what happens to the first resonance length $L_1$?

The first resonance length $L_1$ will be approximately halved. Since $v = f\lambda$ and $v$ is constant, doubling $f$ halves $\lambda$, and since $L_1 \approx \lambda/4$, the required air column length decreases accordingly.

What is the relationship between the first and second resonance lengths in a closed-end tube?

The second resonance length $L_2$ is approximately three times the first resonance length $L_1$ (specifically, $3\lambda/4$ vs $\lambda/4$). However, due to end correction, $L_2$ is usually slightly more than $3 \times L_1$.

Why must the tuning fork be struck with a rubber hammer rather than a hard surface?

A rubber hammer excites the fundamental frequency of the tuning fork while minimizing higher-frequency overtones. A hard strike could produce 'clanging' sounds that make it difficult to identify the primary resonance in the tube.

Define 'Resonance' in the context of this experiment.

Resonance is the phenomenon where the air column is forced to vibrate at its natural frequency by the tuning fork, resulting in a stationary wave with maximum amplitude and a loud audible sound.

How does an increase in air temperature affect the measured resonance lengths?

An increase in temperature increases the speed of sound ($v$). Since $f$ is constant, the wavelength $\lambda = v/f$ must increase, meaning the resonance lengths $L_1$ and $L_2$ will both increase.

What error occurs if the tube is raised too quickly during the experiment?

Raising the tube too quickly may cause the observer to miss the exact point of maximum loudness. This leads to inaccurate recordings of $L_1$ or $L_2$, resulting in a calculated speed of sound that is either too high or too low.

What is the distance between a node and the adjacent antinode in a stationary wave?

The distance between a node and the nearest antinode is one-quarter of a wavelength ($\lambda/4$). In the resonance tube, this corresponds to the distance from the water surface to the open end at the first resonance.

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4. Electrons, Waves & Photons

Determining the Speed of Sound in Air in a Resonance Tube

Summary

The resonance tube experiment is a classic method to determine the speed of sound in air by creating stationary waves within a variable-length air column. By matching the frequency of a tuning fork to the natural frequency of the air column, resonance is achieved, allowing for the calculation of wavelength and subsequently the speed of sound using the wave equation.

1. Definition & Core Concepts

Resonance in an air column occurs when the frequency of an external source, such as a tuning fork, matches one of the natural vibrational frequencies of the air inside the tube.
A stationary wave (or standing wave) is formed by the interference of the incident sound wave from the tuning fork and the wave reflected from the water surface.
The air column acts as a pipe closed at one end (the water surface) and open at the other (where the tuning fork is held).
At resonance, the air molecules vibrate with maximum amplitude, resulting in a significantly louder sound being heard.

Diagram showing the first and second resonance modes in a tube closed at one end. L1 shows a quarter wavelength and L2 shows three-quarters of a wavelength.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions

Determining the Speed of Sound in Air in a Resonance Tube

Q: Why is the subtraction method ($L_2 - L_1$) preferred over using a single resonance length?

Subtracting $L_1$ from $L_2$ eliminates the end correction constant ($e$) from the calculation. Since $L_1 + e = \lambda/4$ and $L_2 + e = 3\lambda/4$, the difference $(L_2 - L_1)$ equals exactly $\lambda/2$, regardless of the value of $e$.

Q: What boundary condition exists at the water surface in the resonance tube?

A displacement node exists at the water surface. This is because the water acts as a fixed boundary where the air molecules are restricted from longitudinal movement, resulting in zero displacement amplitude.

Q: If the frequency of the tuning fork is doubled, what happens to the first resonance length $L_1$?