Superposition of Pulses, Grade 10 Physics
Two or more pulses can pass through the same medium at that same time. The resulting pulse is obtained by using the principle of superposition. The principle of superposition states that the effect of the pulses is the sum of their individual effects. After pulses pass through each other, each pulse continues along its original direction of travel, and their original amplitudes remain unchanged.

Constructive interference takes place when two pulses meet each other to create a larger pulse. The amplitude of the resulting pulse is the sum of the amplitudes of the two initial pulses. This is shown in Figure 5.11.
Definition: Constructive interference is when two pulses meet, resulting in a bigger pulse.

Destructive interference takes place when two pulses meet and cancel each other. The amplitude of the resulting pulse is the sum of the amplitudes of the two initial pulses, but the one amplitude will be a negative number. This is shown in Figure 5.12. In general, amplitudes of individual pulses add together to give the amplitude of the resultant pulse.
Definition: Destructive interference is when two pulses meet, resulting in a smaller pulse.

Figure 5.12: Superposition of two pulses. The left-hand series of images demonstrates destructive interference, since the pulses cancel each other. The right-hand series of images demonstrate a partial cancelation of two pulses, as their amplitudes are not the same in magnitude.

Worked Example: Superposition of Pulses
Question: The two pulses shown below approach each other at 1 m·s$^{−1}$. Draw what the waveform would look like after 1 s, 2 s and 5 s.

Answer
Step 1 : After 1 s

After 1 s, pulse A has moved 1 m to the right and pulse B has moved 1 m to the left.

Step 2 : After 2 s
After 1 s more, pulse A has moved 1 m to the right and pulse B has moved 1 m to the left.

Step 3 : After 5 s

Important: The idea of superposition is one that occurs often in physics. You will see much, much more of superposition!


Exercise: Superposition of Pulses
E - 1. For each of the following pulses, draw the resulting wave forms after 1 s, 2 s, 3 s, 4 s and 5 s. Each pulse is travelling at 1 m·s$^{−1}$. Each block represents 1 m.

E - 2. (a) What is superposition of waves?
(b) What is constructive interference? Use the letter “c” to indicate where constructive interference took place in each of your answers for question 1. Only look at diagrams for t = 3 s.
(c) What is destructive interference? Use the letter “d” to indicate where destructive interference took place in each of your answers for question 1. Only look at diagrams for t = 2 s.

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