Grade 10 Physical Sciences · Waves, Sound and Light

Use the wave equation

Use v = fλ or f = 1/T to find a wave's speed, frequency or wavelength (a 340 m/s sound wave at 170 Hz has λ = 2 m).

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Question 9.4 · November 2024 · Paper 1 · National (DBE) · 2 marks

The graph below shows how the induced current in a generator varies with time. Diagram for this question

9.4 Calculate the frequency at which the coil rotates in the generator.(2)

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More past paper questions: use the wave equation

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3. Question 6.3.1 · November 2024 · Paper 1 · National (DBE) · 3 marks
A stationary listener, standing on the roadside, records the wavelength of the sound emitted by the siren of a police car travelling at a constant velocity.

In the wavelength-time graph below, NOT drawn to scale, $λ_{L}$ is the wavelength of the sound recorded by the listener and $λ_{S}$ is the wavelength of the sound emitted by the siren.

Take the speed of sound in air to be $343$ m·s $^{- 1}$ .
6.3 Calculate the:
6.3.1 Frequency of the sound emitted by the siren(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $v = f λ$
  1 mark · Use the wave equation
2. ✓
  Substitution $343 = f (0, 38)$
  1 mark · Use the wave equation
3. ✓
  Answer $f = 902, 63$ Hz
  1 mark · Use the wave equation
4. Question 6.3 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
A stationary listener records the frequency of the sound emitted by the siren of a police car. When the car which is travelling at a constant velocity of $26$ m·s $^{- 1}$ , approaches the listener, the recorded frequency is $615$ Hz. The car passes the listener at time $t_{1}$ and then moves away from the listener. The recorded frequency now is $526$ Hz.

Ignore the effects of wind.
6.3 Calculate the wavelength of the sound emitted by the police siren.(4)
Show the memo (4 ticks)Memo
1. ✓
  Substitution to find $f_{s}$ $f_{s} = \frac{615 ( 333 , 33 - 26 )}{333 , 33}$
  
  OR $f_{s} = \frac{526 ( 333 , 33 + 26 )}{333 , 33}$
  
  $f_{s} = 567, 03$ Hz
  1 mark · Use the Doppler equation
2. ✓
  Formula $v = f λ$
  1 mark · Use the wave equation
3. ✓
  Substitution $333, 33 = 567, 03 λ$
  1 mark · Use the wave equation
4. ✓
  Answer with unit $λ = 0, 59$ m
  1 mark · Use the wave equation
5. Question 1.2 · November 2023 · Paper 1 · Provincial · 2 marks
1.2 If the velocity of the wave remains constant, the ... increases when the wavelength decreases.(2)
1. A frequency
2. B amplitude
3. C speed
4. D period
Show the memo (1 tick)Memo
1. ✓
  Use v = f lambda with constant v $v = f λ$ . If $v$ stays constant, $f$ and $λ$ are inversely proportional: when $λ$ decreases, $f$ increases. The period $T = \frac{1}{f}$ would decrease, and the speed is given as constant.
  
  Answer: A
  2 marks · Use the wave equation
6. Question 2.4.2 · November 2023 · Paper 1 · Provincial · 3 marks
The diagram below represents a transverse wave with the frequency of $1, 5$ Hz moving from left to right.
2.4 Calculate:
2.4.2 The speed of the wave(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $v = f λ$
  1 mark · Use the wave equation
2. ✓
  Substitution $= (1, 5) (2)$
  1 mark · Use the wave equation
3. ✓
  Answer with unit $= 3$ m·s $^{- 1}$
  1 mark · Use the wave equation

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