a plane progressive wave is represented by y= 6sin 100t-0.5x where all the symbols their usual meaning find ;amplitude,frequency,period,wavelength and the speed
I think you probably mean:
y= 6 sin (100 t - 0.5 x )
Amplitude:
Now that sin function has a range from -1 to plus one.
so if you multiply by 6, you go from -6 to plus 6. In other words 6 is the amplitude of the sin function.
Frequency - DO PERIOD FIRST
Period
How much does t have to change from t = 0 for 100 t to be 2 pi ???
100 T = 2 pi
T = pi / 50 seconds
NOW frequency
f = 1/T = 50 / pi Hertz
Wavelength:
Now how much does x have to change for 0.5 x = 2 pi ????
that x = lambda = 2 pi / 0.5 = 4 pi meters
Speed
goes one wavelength in one period
4 pi meters / ( pi/50 seconds = 200 meters / second