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I don't understand this problem. Any help would be appreciated.

A sinusoidal wave can be described by the following function:

y(x,t) = (15.0 cm) cos( (0.157 m^-1)x + (50.3 s^-1)t + π/4 )

a) What are the amplitude, wave number, wavelength, and period of this wave?

b) Which way is the wave moving and how fast is it moving in that direction?

c) Draw a snapshot graph of the wave at t=0 seconds.

The general equation for a traveling wave is given by:

Y(x,t)=Ao*cos[k*x+w*t+p]

Where:

Ao=maximum amplitude=15.0cm

k=wave number=0.157rad/m

w=angular frequency=50.3rad/s

p=phase angle=pi/4

The wave number k is equal to 2*pi divided by the wavelength lambda therefore:

k=2*pi/lambda therefore lambda=2*pi/k=2*pi/0.157=40m

The angular frequency w is equal to 2*pi/T where T is the period, therefore:

T=2*pi/w=2*pi/50.3=0.125sec

The wave is moving towards the left since w*t is positive.

The velocity of the wave is equal to the product of the frequency and the wavelength:

s=f*lambda

But since period and frequency are mathematical inverses:

T=1/f

The wave speed becomes:

s=lambda/T=40m/0.125s=320m/s moving left

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.