Acoustics Lab: Standing Waves and Speed of Sound
Investigate **Standing Waves** in a closed air column using the resonance tube apparatus. Calculate the **Speed of Sound ($v$)** using the relationship between resonance lengths ($l_1, l_2$) and wavelength ($\lambda$).
Key Equations & Concepts
â–¼The speed of sound ($v$) is related to frequency ($f$) and wavelength ($\lambda$): $$ v = f \cdot \lambda $$
The distance between successive nodes (or antinodes) is half a wavelength ($\lambda/2$). Thus, the difference between the first ($l_1$) and second ($l_2$) resonance lengths gives the wavelength: $$ \lambda = 2(l_2 - l_1) $$
The anti-node forms slightly *outside* the open end. $$ e = \frac{l_2 - 3l_1}{2} \approx 0.3 D $$
Experiment 1: Resonance Length Simulation
Set the tuning fork frequency and observe the resonance lengths ($l_1, l_2$) in the air column.
$\lambda/4$ and $3\lambda/4$ Resonances Found ($v \approx 330 \text{ m/s}$).
Experiment 2: Speed of Sound & Wavelength Challenge
Calculate $\lambda$ and the speed of sound ($v$) using the measured resonance lengths in meters (m).
In the resonance tube, the wave is reflected at the water surface (a **node**) and at the open end (an **anti-node**). Resonance occurs when the air column length ($L$) satisfies $L = (2n-1)\frac{\lambda}{4}$, where $n = 1, 2, 3, \ldots$
Wave Characteristics and Corrections (11th Std)
The speed of sound in air ($v$) depends mainly on the **temperature** and is largely independent of pressure. $v \propto \sqrt{T}$.
A more precise calculation involves the end correction ($e$): $$ v = 2f (l_2 - l_1) $$ The end correction itself is calculated using $e = \frac{l_2 - 3l_1}{2}$.
Sound waves are **longitudinal waves** (vibration parallel to energy transfer). Light waves are **transverse waves** (vibration perpendicular to energy transfer).
Acoustics Lab: Standing Waves and Speed of Sound
Investigate **Standing Waves** in a closed air column using the resonance tube apparatus. Calculate the **Speed of Sound ($v$)** using the relationship between resonance lengths ($l_1, l_2$) and wavelength ($\lambda$).
Key Equations & Concepts
â–¼The speed of sound ($v$) is related to frequency ($f$) and wavelength ($\lambda$): $$ v = f \cdot \lambda $$
The distance between successive nodes (or antinodes) is half a wavelength ($\lambda/2$). Thus, the difference between the first ($l_1$) and second ($l_2$) resonance lengths gives the wavelength: $$ \lambda = 2(l_2 - l_1) $$
The anti-node forms slightly *outside* the open end. $$ e = \frac{l_2 - 3l_1}{2} \approx 0.3 D $$
Experiment 1: Resonance Length Simulation
Set the tuning fork frequency and observe the resonance lengths ($l_1, l_2$) in the air column.
$\lambda/4$ and $3\lambda/4$ Resonances Found ($v \approx 330 \text{ m/s}$).
Experiment 2: Speed of Sound & Wavelength Challenge
Calculate $\lambda$ and the speed of sound ($v$) using the measured resonance lengths in meters (m).
In the resonance tube, the wave is reflected at the water surface (a **node**) and at the open end (an **anti-node**). Resonance occurs when the air column length ($L$) satisfies $L = (2n-1)\frac{\lambda}{4}$, where $n = 1, 2, 3, \ldots$
Wave Characteristics and Corrections (11th Std)
The speed of sound in air ($v$) depends mainly on the **temperature** and is largely independent of pressure. $v \propto \sqrt{T}$.
A more precise calculation involves the end correction ($e$): $$ v = 2f (l_2 - l_1) $$ The end correction itself is calculated using $e = \frac{l_2 - 3l_1}{2}$.
Sound waves are **longitudinal waves** (vibration parallel to energy transfer). Light waves are **transverse waves** (vibration perpendicular to energy transfer).
