Find (a) the amplitude, (b) the wavelength, (c) the period, and (d) the speed of a wave whose displacement is given by y= 1.6 cos( 0.71 x+ 36 t), where x and y are in cm and t is in seconds. part a part complete express your answer using two significant figures. a = 1.6 cm previous answers correct part b part complete express your answer using two significant figures. λ = 8.8 cm previous answers correct part c express your answer using two significant figures. t = s request answer part d express your answer using two significant figures. v = cm/s request answer part e in which direction is the wave propagating?

The expression for the equation of a wave is:
(1)
where
A is the amplitude
is the wave number, with  being the wavelength
x is the displacement
is the angular frequency, with T being the period
t is the time

The equation of the wave in our problem is
(2)
where x and y are in cm and t is in seconds.

a) Amplitude:
if we compare (1) and (2), we immediately see that the amplitude of the wave is the factor before the cosine:
A=1.6 cm

b) Wavelength:
we can find the wavelength starting from the wave number. For the wave of the problem, 

And re-arranging this relationship we find 

c) Period:
we can find the period by using the angular frequency:

By re-arranging this relationship, we find


d) Speed of the wave:
The speed of a wave is given by

where f is the frequency of the wave, which is the reciprocal of the period:

And so the speed of the wave is


e) Direction of the wave:
A wave written in the cosine form as

propagates in the positive x-direction, while a wave written in the form

propagates in the negative x-direction. By looking at (2), we see we are in the second case, so our wave propagates in the negative x-direction.