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.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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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