Math Project : D
Grade 12
Term 3
Student Name: _______________________ ID#: ________________ Student Name: _______________________ ID#: ________________ Section: _____
2012 2013
OBJECTIVES
This project will involve students in: solving real world problems with the use of Trigonometric Identities (sum and difference of angles identities, double angle and half angle identities). evaluating limits algebraically. Task 1: COMMUNICATION Radio waves that pass through the same place at the same time cause interference. Constructive interference occurs when two waves combine to have greater amplitude than either of the component waves.
A radio transmitter sends out two signals, one for voice communication and another for data. Suppose the equation of the voice wave is v = 10 sin(2t 30˚) and the equation of the data wave is d = 10 cos(2t + 60˚). a. Draw a graph of the waves with the use of a program or software when they are combined. b. Analyze and explain what type of interference results from the combination of the two waves.
2
Task 2: Aviation Mach number The Mach number of an airplane is the ratio of the speed of a body to the speed of sound in a particular medium, usually the Earth's atmosphere. Mach Number Object speed Speed of Sound
When an airplane travels faster than the speed of sound, a sonic boom is created or the sound waves form a cone behind the airplane (see figures).
If Ѳ is the measure of the angle at the vertex of the cone, M represents the Mach number; the angle is therefore called the Mach angle. Mach number M can be Ѳ determined using the formula sin . M For example, an aircraft flying through air at twice the speed of sound has a Mach number of 2. The Mach number of an aircraft travelling at a given velocity depends on the altitude of the aircraft and other atmospheric conditions that affect the speed of sound near the aircraft.
Term 3
Student Name: _______________________ ID#: ________________ Student Name: _______________________ ID#: ________________ Section: _____
2012 2013
OBJECTIVES
This project will involve students in: solving real world problems with the use of Trigonometric Identities (sum and difference of angles identities, double angle and half angle identities). evaluating limits algebraically. Task 1: COMMUNICATION Radio waves that pass through the same place at the same time cause interference. Constructive interference occurs when two waves combine to have greater amplitude than either of the component waves.
A radio transmitter sends out two signals, one for voice communication and another for data. Suppose the equation of the voice wave is v = 10 sin(2t 30˚) and the equation of the data wave is d = 10 cos(2t + 60˚). a. Draw a graph of the waves with the use of a program or software when they are combined. b. Analyze and explain what type of interference results from the combination of the two waves.
2
Task 2: Aviation Mach number The Mach number of an airplane is the ratio of the speed of a body to the speed of sound in a particular medium, usually the Earth's atmosphere. Mach Number Object speed Speed of Sound
When an airplane travels faster than the speed of sound, a sonic boom is created or the sound waves form a cone behind the airplane (see figures).
If Ѳ is the measure of the angle at the vertex of the cone, M represents the Mach number; the angle is therefore called the Mach angle. Mach number M can be Ѳ determined using the formula sin . M For example, an aircraft flying through air at twice the speed of sound has a Mach number of 2. The Mach number of an aircraft travelling at a given velocity depends on the altitude of the aircraft and other atmospheric conditions that affect the speed of sound near the aircraft.