Sine Wave Analysis: Frequency, Period, and Effects of Period Reduction

This assignment provides a detailed analysis of sine waves, focusing on the relationship between frequency and period. It begins by defining a sine wave and its general equation, highlighting the roles of amplitude, frequency, phase shift, and vertical shift. The assignment then focuses on calculating the period (T) and frequency (f) of a given sine wave with a frequency of 475 Hz. The period is calculated in milliseconds. Furthermore, the assignment explores the impact of reducing the time period by a factor of 5 and calculates the new frequency in kHz, rounded to three significant figures. References to relevant textbooks are included, enhancing the assignment's credibility. Desklib offers a wealth of similar solved assignments to aid students in their studies.

Running Head: SINE WAVE 1
Sine Wave
Student Name
Institution Name

SINE WAVE 2
Sine Wave
In trigonometry, a sinusoid or a sine wave is the graph of the sine function.
Generally, the sine wave is represented by the curve whose equation is given by, (Bird, 2017):
y= A sin ( B ( x−C ) ) + D
Where A is the amplitude of the sine function
B is the frequency of the sine wave, that is, the number of cycle from 0 to 2 π.
C is the phase shift of the sine wave, that is, the horizontal shift from the origin.
D is the displacement or the vertical shift of the sine wave.
The simplest form of a sine wave is
y= A sin (Bx ¿)¿
Period, T
The period of the sine wave is given by T = 2 π
B (Lial, 2016)
Frequency, f
The frequency of the sine wave is given by f = B
2 π
Relationship between frequency, f and period, T
T = 1
f
The given frequency for this particular sine wave is 475 Hz (cycles per sec)
Calculation of Period, T
T = 1
f
T = 1
475
T =0.0021053 seconds
In milliseconds (ms);
T =0.0021053∗1000=2.1053 milliseconds
T =2.11 ms ¿ 3 significant figures

SINE WAVE 3
Reducing the time period by a factor of 5 and calculating new frequency, f
New Period:
T = 2.11
5
T =0.422 ms
Calculating new frequency of the sine wave;
f = 1
T
f = 1
0.422× 10−3
f =2369.668 Hz
New frequency in kHz and to 3 significant figures;
f = 2369.668
1000 =2.369668 kHz
f =2.37 kHz ¿3 significant figures

SINE WAVE 4
References
Lial, M. L. (2016). College algebra and trigonometry. Pearson Education
Bird, J. (2017). Higher Engineering Mathematics. Routledge.