A plane progressive wave is represented by the

Question

equation: y= 0.1sin(200pi(t)-20pi/15(x)) where
y is the displacement in metres, t is in
seconds and x is the distance from a fixed
origin O in metres. Find (i) the frequency of
the wave, (ii) its wavelength (iii) its speed

Answer 1

In general, you can model this wave as

y=Amplitude sin 2PI/lambda (x-vt)

or
y=amplitude sin 2PI(x/lambda - ft)

so
y=.1 sin 2PI(10x/15 -100t)
f=100

lambda=15/10=1.5 meters

speed=f*lambda

Answer 2

Comparing the eqn with y=asin2pi(ft)-2piX/L. 2piFt=200pit, makin F the subject gives 200pit/2pit which gives F=100HZ. In finding lamda L, 2pix/L=20pix/15, cross multiply n make L the subject. L= 1.5 speed(v)=L*F, 1.5*100=150m/s