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Question
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.

Answer
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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James J. Kovalcin

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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.

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