MATHEMATICS · Multi-part · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry
Problem
During a school talent show, a student singer at point S stands 2.0m in front of a movable, rectangular reflecting screen. A microphone at point M is placed 1.5m to the right of the singer and 2.0m behind the screen. The floor plan is horizontal, and the screen can be rotated about a vertical axis through its centre.
(i) Draw a top-view ray diagram to show how sound from S can reach M after a single reflection from the screen.
(ii) Using geometrical reasoning, determine the angle through which the screen must be turned, measured from the position in which it is perpendicular to the straight line SM, so that the reflected sound reaches the microphone.
(iii) Calculate the total distance travelled by the sound from the singer to the microphone along the reflected path.
(iv) If the speed of sound in air is 340m/s, find the time taken for the sound to travel from the singer to the microphone along this path.