A plane sound wave propagated in air has individual particles which execute a periodic motion such that their displacement y from their rest position at any time t is y=5x10^(-6)sin(800pie(t)+theta). Calculate (i) wavelength. (ii) phase diff in degree between particles 17cm apart.

Answer 1

y =A sin (800 pi t + Th)

when t = 0, 800 pi t = 0
so when 800 pi t = 2 pi
we have done a full cycle.
800 pi T = 2 pi
T = 1/400 second
use velocity of sound now to get
wavelength L = distance = rate * time =(1/400)(velocity of sound)

once you have L
.17 meters /L = fraction of wavelength = fraction of circle/360

Answer 2

you tried but compare the equation with y=asin(2pieft-2piex/Λ)
f-frequency
t-time
Λ-wavelength
by comparing you will solve it easily