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This question is about an experiment to measure the wavelength of microwaves. A microwave transmitter T and a receiver R are arranged on a line marked on the bench. A metal sheet M is placed on the marked line perpendicular to the bench surface. The circuit connected to T and the ammeter connected to R are only shown in the plan view. Figure 1 shows side and plan views of the arrangement. The distance $d$ between T and R is recorded. T is switched on and the output from T is adjusted so a reading is produced on the ammeter as shown in Figure 2. M is kept parallel to the marked line and moved slowly away as shown in Figure 3. The reading decreases to a minimum reading which is not zero. The perpendicular distance $x$ between the marked line and M is recorded. State the phase difference between the sets of waves superposing at R when the ammeter reading is a minimum. Give a suitable unit with your answer. Explain why the minimum reading is not zero when the distance $x$ is measured. When M is moved further away the reading increases to a maximum then decreases to a minimum. At the first minimum position, a student labels the maximum $n = 1$ and records the value of $x$. Several positions of maxima and minima are produced. Describe a procedure that the student could use to make sure that M is parallel to the marked line before measuring each value of $x$. You may wish to include a sketch with your answer. It can be shown that $$nrac{ au}{2} = rac{ ext{sqrt}(x^2 + y^2) - y}{y}$$ where $ au$ is the wavelength of the microwaves and $y$ is the distance defined in Figure 1. The student plots the graph shown in Figure 4. The student estimates the uncertainty in each value of $$rac{ ext{sqrt}(x^2 + y^2)}{y}$$ to be 0.025 m and adds error bars to the graph. Determine - the maximum gradient $G_{max}$ of a line that passes through all the error bars - the minimum gradient $G_{min}$ of a line that passes through all the error bars. Determine $ au$ using your results for $G_{max}$ and $G_{min}$. Determine the percentage uncertainty in your result for $ au$. Explain how the graph in Figure 4 can be used to obtain the value of $y$. You are not required to determine $y$. Suppose that the data for $n = 13$ had not been plotted on Figure 4. Add a tick (\u2713) in each row of Table 1 to identify the effect, if any, on the results you would obtain for $G_{max}$, $G_{min}$, $ au$ and $y$.

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This question is about an experiment to measure the wavelength of microwaves - AQA - A-Level Physics - Question 1 - 2017 - Paper 3

Question 1

This question is about an experiment to measure the wavelength of microwaves. A microwave transmitter T and a receiver R are arranged on a line marked on the bench.... show full transcript

Worked Solution & Example Answer:This question is about an experiment to measure the wavelength of microwaves - AQA - A-Level Physics - Question 1 - 2017 - Paper 3

Step 1

State the phase difference between the sets of waves superposing at R when the ammeter reading is a minimum.

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Answer

The phase difference is 180 degrees, or π radians, as this indicates that the waves interfere destructively at this point.

Step 2

Explain why the minimum reading is not zero when the distance x is measured.

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Answer

The minimum reading is not zero because, even at minimum, some energy is reflected from the metal sheet M, causing interference, leading to a standing wave pattern where a certain amplitude still exists.

Step 3

Describe a procedure that the student could use to make sure that M is parallel to the marked line before measuring each value of x.

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Answer

Use a ruler or a straight edge aligned with the marked line.
Position M so that it directly touches the ruler at a reference point.
Check both ends of M against the ruler to ensure even spacing.
Make small adjustments until M is parallel and visually inspect the alignment before recording values.

Step 4

Determine the maximum gradient Gmax of a line that passes through all the error bars.

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Answer

Calculate the maximum gradient from the data points ensuring the line is steep while still intersecting all error bars. Use the least squares method for accuracy.

Step 5

Determine the minimum gradient Gmin of a line that passes through all the error bars.

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Answer

Calculate the minimum gradient in a similar manner as Gmax but ensure that the line is as shallow as possible while still intersecting all error bars.

Step 6

Determine τ using your results for Gmax and Gmin.

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Answer

Use the relationship $\tau = \frac{2}{G_{max} + G_{min}}$ to find the wavelength τ based on the calculated gradients.

Step 7

Determine the percentage uncertainty in your result for τ.

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Calculate the uncertainty using the formula $\text{Percentage Uncertainty} = \left(\frac{\text{Uncertainty}}{\tau}\right) \times 100$ where the uncertainty can be derived from the errors in Gmax and Gmin.

Step 8

Explain how the graph in Figure 4 can be used to obtain the value of y.

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Answer

The graph can be analyzed to determine the intercept on the y-axis, which corresponds to the distance y when all other variables are accounted for in the equation relating x, y, and τ.

Step 9

Add a tick (✓) in each row of Table 1.

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Answer

Gmax: Not affected
Gmin: Not affected
τ: Increased
y: Increased
Indicate these with checks in Table 1 according to how the absence of data for n=13 influences the results.

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Questions answered

This question is about an experiment to measure the wavelength of microwaves - AQA - A-Level Physics - Question 1 - 2017 - Paper 3

Worked Solution & Example Answer:This question is about an experiment to measure the wavelength of microwaves - AQA - A-Level Physics - Question 1 - 2017 - Paper 3

State the phase difference between the sets of waves superposing at R when the ammeter reading is a minimum.

Explain why the minimum reading is not zero when the distance x is measured.

Describe a procedure that the student could use to make sure that M is parallel to the marked line before measuring each value of x.

Determine the maximum gradient Gmax of a line that passes through all the error bars.

Determine the minimum gradient Gmin of a line that passes through all the error bars.

Determine τ using your results for Gmax and Gmin.

Determine the percentage uncertainty in your result for τ.

Explain how the graph in Figure 4 can be used to obtain the value of y.

Add a tick (✓) in each row of Table 1.

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