11.2 Boundary conditions  (Page 3/3)

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 [link] . In general, amplitudes of individual pulses add together to give the amplitude of the resultant pulse.

Destructive interference is when two pulses meet, resulting in a smaller pulse.

The two pulses shown below approach each other at $1m·s{}^{-1}$ . Draw what the waveform would look like after $1s$ , $2s$ and $5s$ .

1. After $1s$

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

   

2. After $2s$

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

   

3. After $5s$

   After $5s$ , pulse A has moved $5m$ to the right and pulse B has moved $5m$ to the left.

   

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Superposition of pulses

1. For the following pulse, draw the resulting wave forms after $1s$ , $2s$ , $3s$ , $4s$ and $5s$ . Each pulse is travelling at $1m·s{}^{-1}$ . Each block represents $1m$ . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.

   

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2. For the following pulse, draw the resulting wave forms after $1s$ , $2s$ , $3s$ , $4s$ and $5s$ . Each pulse is travelling at $1m·s{}^{-1}$ . Each block represents $1m$ . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.

   

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3. For the following pulse, draw the resulting wave forms after $1s$ , $2s$ , $3s$ , $4s$ and $5s$ . Each pulse is travelling at $1m·s{}^{-1}$ . Each block represents $1m$ . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.

   

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4. For the following pulse, draw the resulting wave forms after $1s$ , $2s$ , $3s$ , $4s$ and $5s$ . Each pulse is travelling at $1m·s{}^{-1}$ . Each block represents $1m$ . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.

   

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5. For the following pulse, draw the resulting wave forms after $1s$ , $2s$ , $3s$ , $4s$ and $5s$ . Each pulse is travelling at $1m·s{}^{-1}$ . Each block represents $1m$ . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.

   

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6. For the following pulse, draw the resulting wave forms after $1s$ , $2s$ , $3s$ , $4s$ and $5s$ . Each pulse is travelling at $1m·s{}^{-1}$ . Each block represents $1m$ . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.

   

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7. What is superposition of waves?
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8. What is constructive interference?
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9. What is destructive interference?
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The following presentation provides a summary of the work covered in this chapter. Although the presentation is titled waves, the presentation covers pulses only.

Exercises - transverse pulses

1. A heavy rope is flicked upwards, creating a single pulse in the rope. Make a drawing of the rope and indicate the following in your drawing:
   1. The direction of motion of the pulse
   2. Amplitude
   3. Pulse length
   4. Position of rest
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2. A pulse has a speed of $\mathrm{2,5}m·s{}^{-1}$ . How far will it have travelled in $6s$ ?
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3. A pulse covers a distance of $75\mathrm{cm}$ in $\mathrm{2,5}s$ . What is the speed of the pulse?
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4. How long does it take a pulse to cover a distance of $200\mathrm{mm}$ if its speed is $4m·s{}^{-1}$ ?
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5. The following position-time graph for a pulse in a slinky spring is given. Draw an accurate sketch graph of the velocity of the pulse against time.

   

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6. The following velocity-time graph for a particle in a medium is given. Draw an accurate sketch graph of the position of the particle vs. time.

   

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7. Describe what happens to a pulse in a slinky spring when:
   1. the slinky spring is tied to a wall.
   2. the slinky spring is loose, i.e. not tied to a wall.
   (Draw diagrams to explain your answers.)
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8. The following diagrams each show two approaching pulses. Redraw the diagrams to show what type of interference takes place, and label the type of interference.

   1. 

   2. 

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9. Two pulses, A and B, of identical shape and amplitude are simultaneously generated in two identical wires of equal mass and length. Wire A is, however, pulled tighter than wire B. Which pulse will arrive at the other end first, or will they both arrive at the same time?
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