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.
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
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 and the value of amplitude A=0.4m.
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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