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harmonic prugIESSIVE(4) Explain the reflection of sound waves fromcurved surface.PROBLEMS FO(1) The equation of a simple harmonic progressivewave is given by y = 4 sin ut (0- cm.Find the displacement and velocity of theparticle at a distance of 50 cm from the originand at the instant 0.1 second (all quantities are inc.g.s. units)(Ans : Displacement = 3.464 cm,Velocity of the particle = 3.14 m/s)(2) The frequency of a tuning fork in 256 |
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Answer» Displacement of particle , y = 4sinπ(t/0.02 - x/75) here t = 0.1 sec and x = 50cm so, y = 4sinπ(0.1/0.02 - 50/75) y = 4sinπ(5 - 2/3) y = 4sinπ(13/3) = 4sin(13π/3) y = 4sin(4π + π/3) = 4sinπ/3 = 4 × √3/2 y = 2√3 = 2 × 1.732 = 3.464 cm y = 4sinπ(t/0.02 - x/75) differentiate with respect to t, dy/dt = (4/0.02)πcosπ(t/0.02 - x/75) v = 200πcosπ(t/0.02 - x/75) at t = 0.1 sec and x = 50cm v = 200πcosπ(0.1/0.02 - 50/75) = 200πcos(13π/3) v = 200πcos(4π + π/3) = 200πcosπ/3 v = 200π × 1/2 = 100π = 314 cm/s or 3.14 m/s |
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