Standing wave

1. Learning Objective 06
Standing waves
Question:
If λis 2πm and A is 1m
a) Please show the fuction of the amplitude of a standing wave.
Hint：A(x)=2Asin(2πx/λ)
b) If the position of a point is 2m, what is the amplitude of that point?
c) What is the location of the first antinode and the first node?
d) If the frequency is 20Hz, what is the wave function?
Hint: D(x,t)=2Asin(2πx/λ)cos(2πt/T)

2. Answer
a) A(x)=2sinx
λis 2π A is 1
b) A(x)=2sinx A
=2sin2=1.82m
c) X=0 for first node
d) D(x,t)=2Asin(2πx/λ)cos(2πt/T)
T=1/f
D(x,t)=2sin(x)cos(40πt)