A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency.
A wave is modeled by the wave function:
y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)]
1. Find the wavelength, wave number, wave velocity, period and wave frequency.
2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s in case the value of amplitude A corresponds to the first letter of your name: letter E
A. A=0.1 m
B. A=0.15 m
C. A=0.2 m
Ç. A=0.25 m
D. A=0.3 m
Dh. A=0.35 m
E. A=0.4 m
Ë. A=0.45 m
F. A=0.5 m
G. A=0.55 m
Gj. A=0.6 m
H. A=0.65 m
I. A=0.7 m
J. A=0.75 m
K. A=0.8 m
L. A=0.85 m
Ll. A=0.9 m
M. A=0.95 m
N. A=1.05 m
Nj. A= 1.1 m
O. A=1.15 m
P. A=1.2 m
Q. A=1.25 m
R. A=1.3 m
Rr. A=1.35 m
S. A=1.4 m
Sh. A=1.45 m
T. A=1.5 m
Th. A=1.55 m
U. A=1.6 m
V. A=1.65 m
X. A=1.7 m
Xh. A=1.75 m
Y. A=1.8 m
Z. A=1.85 m
Zh. A=1.9 m
3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically.
4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows:
y1 (t) = A sin (2πf1t)
y2 (t) = A sin (2πf2t)
5. Find the resultant wave function analytically.
6. Study how the resulting wave behaves in time.
7. Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Comment on the results from the graph and determine the value of the time when the waves are with the same phase and assemble constructively and the time when they are with phase of opposite and interfere destructively.
8. Doing the corresponding numerical simulations show what happens with the increase of the difference between the frequencies of the two waves and vice versa.
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