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Lesson: Chapter 4 — Waves and their applications

Putting the chapter together 2 of 3

The exercise

Exercise 4.1 from the textbook, worked through question by question.

Question 1 — stones in a pond

A group of children drop stones into the still water of a pond and study the waves that spread out

  1. What happens to the energy the waves receive?
  2. A paper boat is placed on the water and a stone dropped a little way from it. What do you observe about the boat, and what does it show?
  3. Draw a diagram to show what happens at the water surface.
  4. Which kind of mechanical wave are the waves on the water surface?
  5. How do these waves differ from the sound waves in air?

The answer

  1. It is carried outward across the water surface, away from where the stone fell.
  2. The boat bobs up and down where it is; it is not carried away. The wave carries energy, but not the water.
  3. Concentric circles spreading out from the point where the stone fell, as in Figure 4.1.
  4. Transverse waves.
  5. In the water waves the particles move at right angles to the direction of travel; in sound waves in air they move parallel to it, because sound is longitudinal.

Question 2 — a vibrating metal strip

A metal strip AB is clamped at B to a table, and end A is made to vibrate

Figure to be added

The metal strip AB standing upright, clamped at B to the top of a table.
  1. Draw a diagram of one vibration, using C and D for the greatest displacements.
  2. Using A, C and D, explain what the amplitude of the vibration is.
  3. If the strip makes 50 vibrations in 5 seconds, find its frequency.
  4. The vibrating strip makes compressions and rarefactions in the air. Which quantity equals the distance between two neighbouring compressions?
  5. Which characteristic depends on (a) frequency, (b) amplitude, and (c) which lets the same note be told apart on different instruments?

The answer

  1. The strip swings from its rest position A out to C on one side, back through A to D on the other, and back to A.
  2. The amplitude is the greatest displacement from the rest position: the distance from A to C, which equals the distance from A to D.
  3. frequency = 50 ÷ 5 s = 10 Hz
  4. The wavelength of the sound wave.
  5. (a) pitch, (b) loudness, (c) quality of sound.

Question 3 — electromagnetic waves

Electromagnetic waves need no particles of a medium to travel

  1. Write three properties of electromagnetic waves.
  2. What is the angle (a) between the electric and magnetic fields, and (b) between those fields and the direction the wave travels?

The answer

  1. They are not affected by external electric and magnetic fields; they need no medium; in a vacuum they travel at 3 × 108 m s-1.
  2. (a) 90°; (b) 90° — the wave travels at right angles to both fields.

Question 4 — a wave on a string

Part of a string carrying a transverse wave is shown, with points A, B, C, D and E

Figure to be added

A sine wave along a horizontal line: A on the line at the start, D at the first crest, B and C where the wave crosses the line, and E at the next crest.
  1. Which quantity equals the distance between D and E?
  2. Which other two letters are the same quantity apart?

The answer

  1. The wavelength — D and E are neighbouring crests.
  2. A and C: both are on the line with the particle moving the same way, one full wave apart.

Question 5 — the school music room

The school music room has many instruments

  1. Name two each of string, percussion and wind instruments you might find there.
  2. Give the factors that decide the frequency of the note from (a) a string instrument (two), (b) a percussion instrument (two), (c) a wind instrument (one).

The answer

  1. String: violin, guitar. Percussion: tabla, drum. Wind: flute, trumpet.
  2. (a) the length of the vibrating string and its tension (or its mass per unit length); (b) the area of the skin and its tension; (c) the length of the air column.

Question 6 — explain scientifically

Explain these scientifically

  1. A ringing bell stops ringing when you hold it in your hand.
  2. A flute sounds a different pitch with all its holes closed than with a hole left open.
  3. Lightning and thunder happen together, yet we hear the thunder a little after we see the flash.

The answer

  1. Sound is produced by vibration. Holding the bell stops it vibrating, so it stops producing sound.
  2. The pitch of a wind instrument depends on the length of its vibrating air column. Opening a hole shortens the column, which raises the frequency and so the pitch.
  3. Light travels at 3 × 108 m s-1 and sound at only about 330 m s-1, so the sound takes much longer to cover the same distance.