Applications of Sinusoidal Functio= ns
Problem 1: AC Voltages, Current, and Power.
a) Most household outlets have a voltage that oscillates sinusoidal with a frequenc= y of 60 hertz (1hz=3D1 cycle/second) and a voltage am= plitude of 170 Volts. Write this out = as a sinusoidal function.
b) Ohm&#= 8217;s law states the V=3DIR for conductors, where I is= the current and R is the resistance. If a light bulb has a R=3D20 ohms, write down the sinusoidal function describing the electric current through the light bulb.= It will be in amps.
c) If the power dissipated by the light bulb is P=3DIV= , write down the sinusoidal function describing this. It will be in watts. Is it ever negative?
Problem 2: Sound Waves. Sound waves are oscill= ations of air pressure that propagate through the air. Atmospheric pressure i= s 14.7 lbs/in2
a) Mosquito’s wings beat with a frequency of = 600 cycles/second. If the = speed of sound is 340 meters/second and the fluctuations in pressure are of the magnitude 0.2 lbs/in2 write down the sinusoidal equation describ= ing the sound wave as it travels through the air.