Two waves in one string are described by the wave functions: y_

ffortunyu

ffortunyu

Answered question

2021-12-06

Two waves in one string are described by the wave functions:
y1=(3.0cm)cos(4.0×1.6t)
y2=(4.0cm)sin(5.0×2.0t)
where y and x are in centimeters and t is inseconds. Find the superposition of the waves y1+y2 at the points (a) x=1.00, t=1.00; (b)x=1.00, t=.500; and (c) x= 0.500, t=0.

Answer & Explanation

Sculd1987

Sculd1987

Beginner2021-12-07Added 19 answers

Given 
two waves are described as 
y1=(3.0cm)cos(4.0x-1.6t)&y2=(4.0cm)sin(5.0x-2.0t) 
a) 
At x = 1cm & t = 1.0s 
we have 
y=y1+y2 
=(3.0cm)cos(4.011.61)+(4.0cm)sin(5.012.01) 
=3cos(2.4rad)+4sin(3rad) 
=-2.212 + 0.5645 
=-1.647cm 
b) 
At x=1.00, t=0.500 
we have 
y=y1+y2 
=(3.0cm)cos(4.011.60.5)+(4.0cm)sin(5.012.00.5) 
=-2.995 +(- 3.027) 
=-6.022cm 
c) 
At x= 0.500, t=0 
we have 
y=y1+y2 
=(3.0cm)cos(4.00.51.60)+(4.0cm)sin(5.00.52.00) 
=- 1.248 + 2.394 
=1.146cm

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