Question

a simple harmonic progressive wave is given by equation y =0.1sin 4π[50t -0.1x] in SI unit. Find frequency, amplitude and velocity of wave.... GIVE ANS...

Answer 1

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

Answer 2

ans....

frequency is 25/π I.e. 7.9Hz

Amplitude is 0.1m

velocity is 39.78m/s