MESSAGE MY INSTRUCTOR FULL SCREEN PRINTER VERSION BACK Chapter 16, Problem 089 T

Question

MESSAGE MY INSTRUCTOR FULL SCREEN PRINTER VERSION BACK Chapter 16, Problem 089 Two waves are described by 1- 0.37 sin[at(3x 180t)] and y2 0.37 sin[7 (3x 180t) T/5], where y1, y2, and x are in meters and t is in seconds. When these two waves are combined, a traveling wave is produced. What are the (a) amplitude, (b) wave speed, and (c) wavelength of that traveling wave? (a) Number Units (b) Number Units (c) Number Click if you would like to show work for this question: Open Show Work Question Attempts o of 5 used Copyright o 20oo-2017 by John wiley & Sons, inc. or related companies. All rights reserved.

Explanation / Answer

y1+y2=0.37*sin(pi*(3*x-180*t))+0.37*sin(pi*(3*x-180*t)+(pi/5))

=2*0.37*sin(pi*(3*x-180*t)+(pi/10))*cos(pi/10)

[using the formula:

sin(C)+sin(D)=2*sin((C+D)/2)*cos((C-D)/2))

]

y1+y2=0.70378*sin(3*pi*x-180*pi*t+(pi/10))

part a:

amplitude=0.70378 m

part b:

comparing argument of sine function with the general wave function : k*x-w*t

we get k=3*pi

==>2*pi/wavelength=3*pi

==>wavelength=0.67 m

angular frequency=w=180*pi

==>2*pi*frequency=180*pi

==>frequency=90 Hz

so speed=wavelength*frequency=0.67*90=60 m/s

part c:

wavelength =0.67 m

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