12.2 Boundary conditions  (Page 5/5)

Superposition and interference

1. For each labelled point, indicate whether constructive or destructive interference takes place at that point.

   

   

2. A ride at the local amusement park is called "Standing on Standing Waves". Which position (a node or an antinode) on the ride would give the greatest thrill?
   
3. How many nodes and how many anti-nodes appear in the standing wave below?

   

4. For a standing wave on a string, you are given three statements:
   1. you can have any $\lambda$ and any $f$ as long as the relationship, $v=\lambda ·f$ is satisfied.
   2. only certain wavelengths and frequencies are allowed
   3. the wave velocity is only dependent on the medium
   Which of the statements are true:
   1. A and C only
   2. B and C only
   3. A, B, and C
   4. none of the above
5. Consider the diagram below of a standing wave on a string 9 m long that is tied at both ends. The wave velocity in the string is 16 m $·$ s ${}^{-1}$ . What is the wavelength?

   

Summary

1. A wave is formed when a continuous number of pulses are transmitted through a medium.
2. A peak is the highest point a particle in the medium rises to.
3. A trough is the lowest point a particle in the medium sinks to.
4. In a transverse wave, the particles move perpendicular to the motion of the wave.
5. The amplitude is the maximum distance from equilibrium position to a peak (or trough), or the maximum displacement of a particle in a wave from its position of rest.
6. The wavelength ( $\lambda$ ) is the distance between any two adjacent points on a wave that are in phase. It is measured in metres.
7. The period ( $T$ ) of a wave is the time it takes a wavelength to pass a fixed point. It is measured in seconds (s).
8. The frequency ( $f$ ) of a wave is how many waves pass a point in a second. It is measured in hertz (Hz) or $s{}^{-1}$ .
9. Frequency: $f=\frac{1}{T}$
10. Period: $T=\frac{1}{f}$
11. Speed: $v=f\lambda$ or $v=\frac{\lambda }{T}$ .
12. When a wave is reflected from a fixed end, the resulting wave will move back through the medium, but will be inverted. When a wave is reflected from a free end, the waves are reflected, but not inverted.

Exercises

1. A standing wave is formed when:
   1. a wave refracts due to changes in the properties of the medium
   2. a wave reflects off a canyon wall and is heard shortly after it is formed
   3. a wave refracts and reflects due to changes in the medium
   4. two identical waves moving different directions along the same medium interfere
2. How many nodes and anti-nodes are shown in the diagram?

   

3. Draw a transverse wave that is reflected from a fixed end.
   
4. Draw a transverse wave that is reflected from a free end.
   
5. A wave travels along a string at a speed of $\mathrm{1,5}m·s{}^{-1}$ . If the frequency of the source of the wave is 7,5 Hz, calculate:
   1. the wavelength of the wave
   2. the period of the wave
6. Water waves crash against a seawall around the harbour. Eight waves hit the seawall in 5 s. The distance between successive troughs is 9 m. The height of the waveform trough to crest is 1,5 m.

   

   1. How many complete waves are indicated in the sketch?
   2. Write down the letters that indicate any TWO points that are:
      1. in phase
      2. out of phase
      3. Represent ONE wavelength.
   3. Calculate the amplitude of the wave.
   4. Show that the period of the wave is 0,67 s.
   5. Calculate the frequency of the waves.
   6. Calculate the velocity of the waves.