Question

A transverse wave propagating along x-axis is represented by y(x, t) = 8 sin (0.5 pi x - 4 pi t - pi/4) where x is in metre and t is in second.The speed of the wave is

Answer 1

speed of wave=wavelength x frequency
=wavelength/time period
now we know
from of wave equation
y=Asin{ (2pi/lemda)x+_(2pi/T)t+$)
where A is amplitude of wave , lemda is wavelength ,T is time period and $ is phase constant.
now compare both equation
then
2pi/lemda=0.5pi
lemda=4m
again
2pi/T=4pi
T=1/2sec
hence speed of wave=4/(1/2)=8m/sec