nsider the physical sign when $e > 0$.\n\nWith an end correction, the antinode is outside the tube, meaning the effective length is longer than the physical length:\n\n$$x_1 + e = \\frac{\\lambda}{4} \\implies x_1 = \\frac{\\lambda}{4} - e$$\n$$x_2 + e = \\frac{3\\lambda}{4} \\implies x_2 = \\frac{3\\lambda}{4} - e$$\n\nBecause $e > 0$, the physical tube lengths $x_1$ and $x_2$ are slightly shorter than their ideal fractions of a wavelength. Since $x_1$ is shifted down by $e$, and $x_2$ is also shifted down by $e$, the value of $3x_1$ decreases more than $x_2$ does. Thus, we expect:\n\n$$x_2 > 3x_1 \\implies x_2 - 3x_1 > 0$$\n\nTherefore, the expression for $e$ must be positive, which rules out Option B as it would yield a negative value ($-e$).","highlights":[{"text":"eliminated","index":1,"location":"eliminate"}]},{"type":"text","order":4,"title":"Confirm correct answer","content":"Substituting our expressions into Option A confirms this:\n\n$$\\frac{x_2 - 3x_1}{2} = \\frac{\\left(\\frac{3\\lambda}{4} - e\\right) - 3\\left(\\frac{\\lambda}{4} - e\\right)}{2} = \\frac{2e}{2} = e$$\n\nThis perfectly matches our end correction $e$.","highlights":[{"text":"correct answer","index":0,"location":"option"}]}]}],"generatedAt":"2026-06-09T16:14:11.684Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"7e4d167e-12f2-4998-9ed0-095af32c977a","revisionId":"abc55afd-2c8e-4c6d-9fad-293ec4cf0d28","questionNumber":null,"questionType":"LA","specification":"","difficulty":4,"difficultyBand":"medium","totalMarks":7,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"be3a9dac-ba04-4767-8ffa-d7a123650bea","label":null,"content":"Describe a school laboratory experiment using microwave equipment to determine the speed of electromagnetic waves.\n\nIn your answer you should:\n- include a description of the experimental setup and a labelled diagram\n- state the measurements that must be taken\n- explain how these measurements are used to determine the speed of the microwaves.","markscheme":"- Describes or draws a setup where a microwave transmitter is aimed at a flat metal reflector plate to produce a stationary wave pattern through the superposition of incident and reflected waves B1\n- Identifies the use of a movable detector/probe placed between the transmitter and the reflector to locate nodes (minima) and antinodes (maxima) B1\n- Measures the positions of successive minima (or maxima) along the line of the waves using a metre ruler M1\n- States that the frequency $f$ of the microwave transmitter must be recorded B1\n- Explains that the distance $d$ between two adjacent nodes is equal to half the wavelength, so $\\lambda = 2d$ M1\n- Describes measuring the distance across several minima (e.g. $N$ minima) and dividing by $N-1$ to obtain a more accurate average spacing $d$ M1\n- Calculates the speed of the microwaves using the wave equation $c = f\\lambda$ A1","marks":7,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"standingwaves","label":"Stationary Wave Method","steps":[{"type":"text","order":0,"title":"Set up the apparatus","content":"To determine the speed of electromagnetic waves using microwaves, we set up a stationary wave pattern in the laboratory.\n\n### Experimental Setup\n1. Place a **microwave transmitter** on a flat surface, pointing towards a flat, vertical **metal reflector plate**.\n2. When the transmitter is turned on, it emits microwave radiation. These waves travel to the plate, reflect back, and travel in the opposite direction.\n3. The superposition of the incident and reflected waves of the same frequency and amplitude creates a **stationary wave** pattern between the transmitter and the reflector plate.\n\n### Diagram representation:\n$$\\text{Transmitter} \\xrightarrow{\\quad\\text{Incident wave}\\quad} \\text{Movable Probe} \\xleftarrow{\\quad\\text{Reflected wave}\\quad} \\text{Metal Reflector}$$"},{"type":"text","order":1,"title":"Detect nodes an

Progressive and stationary waves

Question 21

Progressive and stationary waves Questions

Progressive and stationary waves

Question 21

Progressive and stationary waves Questions