Question

Plz help

Write the expressions for the following descriptions.

16. A 10 volt peak sine wave at 20 Hz
17. A 5 peak to peak sine wave at 100 Hz with a -1 VDC offset
18. A 10 volt RMS sine wave at 1 kHz lagging by 40 degrees
19. A 20 volt peak sine wave at 10 kHz leading by 20 degrees with a 5 V DC offset

Answer 1

Hi, Josh,
Let's take a quick look at Problem 16 first. We want to write an expression such as y = a*sin (bt) to represent this 10-volt peak sine wave with frequency 20 Hz.
The challenge in these questions lies in discerning the value of the coefficient b in y = a*sin (bt). To get started, I did an Internet search for "sine wave frequency," and through doing so came up with the following (among others!): http://www.mathopenref.com/trigsinewaves.html
I'd suggest you spend a minute or two reading that.
This article reminded me that "20 Hz" translates into "the number of complete cycles of the sine wave per second is 20: 20 cycles per second => \[20 Hz =\frac{ 20 cycles }{ 1 second }\]
If 20 cycles take place in 1 second, then doesn't it seem reasonable to state that the period (the length of one cycle) is 1/20 th of a second?
I swear by the the following relationship for the period of a sine wave: P=(2pi)/b.
If the period P is (1/20)th of a second, then (1/20)=(2p)/b. Solve for b.

Now that "10 volt peak" in the problem statement signifies that the maximum height (above zero) that the sine wave reaches is 10 volts. In other words, the amplitude, a, of the sine wave is 10 volts.

Then represent the sine wave of Problem 16 by y = a*sin (bt), where a is the amplitude, b is the frequency, and t is the only variable and represents time.
Substituting a=10 volts and b=40pi,

y = (10 v.)*sin (40pi*t).

This argument is a bit roundabout; I'm sure there are faster ways to come up with b (which I call the "frequency" of the sine wave.

Now for a little checking: Since the period, P, of a sine (or cosine) wave is 2pi/b, let's see whether our (2pi)/b correctly predicts the period of the sine wave in question:
\[\frac{ 2\pi }{ 40\pi }=\frac{ 1 }{ 20 }\sec.\]

This is correct, because 20 Hz implies that we have 20 cycles of the sine wave in 1 sec. Does (1sec/20) times 20 equal 1 sec? Yes. Case closed.

When in doubt, please take advantage of your textbook, course handouts and/or Internet articles to double-check the meaning of the vocabulary involved and to find examples.

Answer 2

All the best to you. MM

Answer 3

tnx mathmale your d best

Answer 4

Gee, thanks! :)