An oscilloscope is a device that presents pictures of sound waves.The function y=0.002sin(200piex) describes the sound produced by a tuning fork, where x represents the time in seconds.
a)What is the amplitude of the given function?
b)What is its period?
c)Copy and complete this table, finding values of y to four decimal places:
x| 0 |1/800 |2/800 |3/800 |4/800 |5/800 |6/800 |7/800 |8/800
y|___ | ____ | ____ | ____ | ____ | ____ | ____ | ____ |
a)What is the amplitude of the given function?
b)What is its period?
c)Copy and complete this table, finding values of y to four decimal places:
x| 0 |1/800 |2/800 |3/800 |4/800 |5/800 |6/800 |7/800 |8/800
y|___ | ____ | ____ | ____ | ____ | ____ | ____ | ____ |
-
amplitude is the 0.002 in front of sin,
period is 2π / 200π = 1/100
notice 8/800 = 1/100, so you're looking at 1 period divided into 8 parts
so y = 0 when x = 0, 4/800, and 8/800.
halfway between those sine hits its high and low, so
y = 0.002 when x = 2/800 and y = -0.002 when x = 6/800
and halfway between those the value of sine is ±½√2 (times the amplitude)
so 0.001(1.414) = 0.001414 when x = 1/800 and when x = 3/800, and
-0.001414 when x = 5/800 and when x = 7/800.
nice problem, no calculator needed (if you learned math BC)
period is 2π / 200π = 1/100
notice 8/800 = 1/100, so you're looking at 1 period divided into 8 parts
so y = 0 when x = 0, 4/800, and 8/800.
halfway between those sine hits its high and low, so
y = 0.002 when x = 2/800 and y = -0.002 when x = 6/800
and halfway between those the value of sine is ±½√2 (times the amplitude)
so 0.001(1.414) = 0.001414 when x = 1/800 and when x = 3/800, and
-0.001414 when x = 5/800 and when x = 7/800.
nice problem, no calculator needed (if you learned math BC)