A-Level OCR Physics A 3. Waves: A student is investigating stati

Question

A student is investigating stationary waves in the air column inside a tube, using the apparatus shown in Fig. 5.1.

The loudspeaker emits sound of frequency $f$ and wavelength $\lambda$. The tube is initially fully immersed in the water. The student then slowly raises the tube until the oscilloscope trace shows its first maximum. A stationary wave of fundamental frequency $f$ is produced in the air column. When this occurs, the student measures the length $l$ of the tube above the water level.

(a) Explain how a stationary wave of fundamental frequency is produced and state the relationship between $l$ and $\lambda$.

(b) Theory suggests that $f$ and $\lambda$ are related by the equation $4(l + k) = \frac{v}{f}$, where $v$ is the speed of sound in air and $k$ is a constant.

The student measures corresponding values of $f$ and $\lambda$ and plots a graph of $\frac{1}{f}$ against $\frac{1}{\lambda}$. The data points, error bars and line of best fit drawn by the student are shown in the graph below.

(i) Show that the line of best fit has gradient = $\frac{v}{4}$ and $y$-intercept = $-k$.

(ii) Calculate $v$ from the gradient of the line of best fit.

(c) The experiment is repeated using the same tube and an unlabelled tuning fork, as shown in Fig. 5.2.

The distance $l$ is measured as 22 cm.

(i) Use the line of best fit on the graph to estimate $F$.

(ii) The percentage uncertainty in the value of $F$ can be written as $100 \frac{\Delta F}{F}$ where $\Delta F$ is the absolute uncertainty in $F$. Use the rules for combining uncertainties to write an expression for the percentage uncertainty in the value of $F$ in terms of $v$ and its absolute uncertainty $\Delta v$, $l$ and its absolute uncertainty $\Delta l$, and $k$ and its absolute uncertainty $\Delta k$.

A student is investigating stationary waves in the air column inside a tube, using the apparatus shown in Fig - OCR - A-Level Physics A - Question 5 - 2021 - Paper 1

Worked Solution & Example Answer:A student is investigating stationary waves in the air column inside a tube, using the apparatus shown in Fig - OCR - A-Level Physics A - Question 5 - 2021 - Paper 1

Explain how a stationary wave of fundamental frequency is produced and state the relationship between l and λ.

Show that the line of best fit has gradient = v/4 and y-intercept = -k.

Calculate v from the gradient of the line of best fit.

Use the line of best fit on the graph to estimate F.

Write an expression for the percentage uncertainty in the value of F.

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