1. Physics 101 LO6,
Yungee Jung

2. Standing Wave- What is it?
 Two harmonic waves, with same amplitude,
wavelength, and frequency that are moving in opposite
directions
 Unlike a traveling wave, the “x” (position) is in a sin
function while the “t” (time) is in the cosine function.
 Full equation of Standing wave:
D(x,t) = 2A(kx)cos(wt) (where “w” is omega)

3. Where did this equation come
from?
 There is a position dependent Amplitude : A(x)
Which is :
A(x) = 2Asin(kx)
Therefore, replacing this in the original Standing wave
equation of (D(x,t) = 2A(kx)cos(wt) )
We can simplify the equation to:
D(x,t) = A(x)cos(wt)

4. The Amplitude function with
postion
Now more onto the Amplitude equation:
- Amplitude is a sine function! So, there are certain
points where there is zero amplitude.
- These “zero” points are called NODES
In opposite, when the Amplitude is at its maximum, it is
called the ANTINODES.

5. Question time!
The equation of the amplitude of a standing wave is :
A(x) = (0.50 cm)sin(3.00x)
Find the:
a) Amplitude and wavelength of the consituent
travelling wave
b) Location of the first 2 nodes and first 2 antinodes

6. Solution to problem part A
Since A(x) = 2Asin(kx)
And from previous equations, k is equal to 2π/λ
Therefore, 2A must equal 0.50 cm and 2π/λ equals 3
rads/m
2A = 0.50cm
A= 0.25 cm 2π/3=λ λ=2.094m

7. Solution to part B
 Calculating nodes: at nodes, A(x) =0.
 So, nodes occur when sin((2π/λ )x)=0
Since sin(0)=0, (2π/λ )x = 0
Using the λ=2.094m from part a,
The equation of position of nodes is:
0, ± λ/2, ±λ, (for the first 3 nodes positions)

8. Solution to part B continued
Therefore, the positions of the first 2 nodes are:
x=0, x= 2.094/2
The positions of the first two NODES are 0 and
1.047m.

9. Antinode equation(Solution to part
B)
At the antinode of a standing wave, the amplitude A(x) =
±2A
- This occurs at the sin max/ min, which is ±1
The equation for the first two antinode positons are:
x= ±λ/4, ±3λ/4
Therefore, using λ=2.094,
The first 2 antinode positions are x =0.524 and 1.571m