What is the experimental setup and procedure for measuring the speed of sound in trapped air using a tuning…

Question

What is the experimental setup and procedure for measuring the speed of sound in trapped air using a tuning fork and a resonance column?

ScanSolve AI Tutor · Accepted Answer

Here is the solution for the experiment "Measuring the Speed of Sound in Trapped Air":

Diagram

\begin{tikzpicture}[scale=0.8]
    % Beaker
    \draw (0,0) -- (0,5) -- (4,5) -- (4,0) -- cycle;
    \draw[fill=blue!20] (0.1,0.5) rectangle (3.9,2.5); % Water level
    \node at (2,1.5) {Water};

    % Pipe
    \draw[thick] (1.5,2.5) -- (1.5,6.5);
    \draw[thick] (2.5,2.5) -- (2.5,6.5);
    \draw[thick] (1.5,6.5) arc (180:0:0.5); % Top arc
    \draw[thick] (1.5,2.5) arc (180:360:0.5); % Bottom arc (hidden)
    \node at (2,4.5) {Pipe};

    % Air column
    \draw[dashed] (2.5,2.5) -- (2.5,6.5); % Inner line for air column
    \draw[<->] (2.8,2.5) -- (2.8,6.5) node[right, midway] {$L$};
    \node at (2,5.5) {Air Column};

    % Tuning Fork
    \draw[thick] (5,6) -- (5,6.5);
    \draw[thick] (5,6.5) -- (5.5,6.5);
    \draw[thick] (5,6.5) -- (4.5,6.5);
    \draw[thick] (5,6) -- (5,5.5);
    \draw[thick] (5,5.5) arc (90:270:0.25);
    \node at (5,7) {Tuning Fork};

    % Sound waves
    \draw[decorate,decoration={snake,amplitude=.5mm,segment length=2mm}] (4.5,6.5) -- (2,6.5);
    \draw[decorate,decoration={snake,amplitude=.5mm,segment length=2mm}] (5.5,6.5) -- (2,6.5);
\end{tikzpicture}

Procedure

Set up the apparatus by placing the plastic pipe vertically into a tall measuring cylinder partially filled with water.
Measure the room temperature using a thermometer and the internal diameter of the pipe using a vernier caliper (or use the given value).
Strike a tuning fork of known frequency (e.g., $512 \text{ Hz}$ ) gently on a rubber pad and hold it horizontally just above the open end of the pipe.
Adjust the water level in the pipe by slowly raising or lowering the pipe in the cylinder until a loud resonant sound is heard. This corresponds to the first resonance.
Measure the length of the air column ( $L_1$ ) from the top of the pipe to the water surface using a metre rule. Record this value.
Continue to lower the water level until a second, louder resonance is heard.
Measure the length of this air column ( $L_2$ ) from the top of the pipe to the water surface. Record this value.
Repeat steps 4-7 several times to obtain multiple readings for $L_1$ and $L_2$ , and calculate their average values.

Observations/Results

Frequency of tuning fork, $f = 512 \text{ Hz}$
Internal diameter of the pipe, $d = 2.5 \text{ cm} = 0.025 \text{ m}$
Room temperature, $T = 25^\circ \text{C}$

Reading	First Resonance Length ( $L_1$ )	Second Resonance Length ( $L_2$ )
1	$16.1 \text{ cm}$	$49.9 \text{ cm}$
2	$16.2 \text{ cm}$	$49.8 \text{ cm}$
3	$16.0 \text{ cm}$	$50.0 \text{ cm}$
Average	$16.1 \text{ cm}$	$49.9 \text{ cm}$

Average $L_1 = 16.1 \text{ cm} = 0.161 \text{ m}$
Average $L_2 = 49.9 \text{ cm} = 0.499 \text{ m}$

Calculations

Calculate the wavelength ( $\lambda$ ) of the sound wave.
The difference between consecutive resonance lengths corresponds to half a wavelength:
$\lambda = 2(L_2 - L_1)$
Substitute the average values:
$\lambda = 2(0.499 \text{ m} - 0.161 \text{ m})$ $\lambda = 2(0.338 \text{ m})$ $\lambda = 0.676 \text{ m}$
Calculate the speed of sound ( $v$ ) using the formula $v = f\lambda$ .
$v = 512 \text{ Hz} \times 0.676 \text{ m}$ $v = 346.112 \text{ m/s}$
Calculate the theoretical speed of sound at the measured temperature for comparison.
The speed of sound in air at temperature $T$ (in $^\circ \text{C}$ ) is approximately given by:
$v_T = 331 \text{ m/s} + (0.6 \text{ m/s/}^\circ \text{C} \times T)$
For $T = 25^\circ \text{C}$ :
$v_{25} = 331 \text{ m/s} + (0.6 \text{ m/s/}^\circ \text{C} \times 25^\circ \text{C})$ $v_{25} = 331 \text{ m/s} + 15 \text{ m/s}$ $v_{25} = 346 \text{ m/s}$
Inference

The speed of sound in air at $25^\circ \text{C}$ was determined to be approximately $346.1 \text{ m/s}$ .

Conclusion

The experiment successfully determined the speed of sound in air at room temperature ( $25^\circ \text{C}$ ) to be $\boxed{\text{346.1 m/s}}$ . This value is in close agreement with the theoretical value of $346 \text{ m/s}$ for sound in air at $25^\circ \text{C}$ .

Precautions
- Ensure the tuning fork is struck gently on a rubber pad to produce a clear, pure tone and avoid damage.
- Hold the vibrating tuning fork horizontally and as close as possible to the open end of the pipe to maximize the transfer of sound energy.
- Ensure the pipe is held perfectly vertical to maintain a consistent and accurate length of the air column.
- Take multiple readings for the resonance lengths ( $L_1$ and $L_2$ ) and calculate their averages to minimize random errors.
- Accurately identify the point of maximum loudness for resonance, as this indicates the precise resonance length.
- Read the metre rule at eye level to avoid parallax errors when measuring the air column lengths.
- Record the room temperature accurately using a thermometer, as the speed of sound is temperature-dependent.

What is the experimental setup and procedure for measuring the speed of sound in trapped air using a tuning fork and a resonance column?

Answer

Step-by-step solution

Calculate the wavelength ( $\lambda$ ) of the sound wave.

Calculate the speed of sound ( $v$ ) using the formula $v = f\lambda$ .

Calculate the theoretical speed of sound at the measured temperature for comparison.

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More Physics Questions

What is the experimental setup and procedure for measuring the speed of sound in trapped air using a tuning fork and a resonance column?

Answer

Step-by-step solution

Calculate the wavelength (λ\lambdaλ) of the sound wave.

Calculate the speed of sound (vvv) using the formula v=fλv = f\lambdav=fλ.

Calculate the theoretical speed of sound at the measured temperature for comparison.

Try one yourself

Still stuck on this one?

More Physics Questions

Calculate the wavelength ( $\lambda$ ) of the sound wave.

Calculate the speed of sound ( $v$ ) using the formula $v = f\lambda$ .