Sound and oscillation

A student claps 51 m from a large wall and hears the echo 0.30 s later. What speed of sound does this measurement give?

1. A

   85 m s⁻¹

2. B

   170 m s⁻¹

3. C

   340 m s⁻¹

4. D

   680 m s⁻¹

1. a

   Select and show Select the correct speed and show why the travel distance is not 51 m.

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   Correct choiceC

   1. 1

      Selects option C: the measured speed of sound is 340 m s⁻¹.

   2. 2

      Uses total sound path = 2 × 51 = 102 m because sound travels to the wall and back.

   3. 3

      Calculates speed = 102 ÷ 0.30 = 340 m s⁻¹.

The same pendulum is released from different angles. A student times ten complete oscillations for each angle.

1. a

   Calculate Calculate the period at 10° and at 40°.

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   1. 1

      Calculates period at 10° = 12.6 ÷ 10 = 1.26 s.

   2. 2

      Calculates period at 40° = 13.4 ÷ 10 = 1.34 s.

2. b

   Evaluate A simple model says the period is independent of amplitude for small angles. Evaluate the data against this model.

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   1. 1

      Notes that 5°–20° times are nearly constant at 12.6–12.7 s for ten oscillations.

   2. 2

      Notes a clearer increase at 30° and especially 40°.

   3. 3

      Concludes that the model is supported for the smaller tested angles but becomes less reliable as angle increases.

3. c

   Improve Propose how to decide more confidently where the small-angle approximation ceases to be useful.

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   1. 1

      Uses more angle values, especially between 20° and 40°.

   2. 2

      Repeats timings at each angle and calculates means and spread or uncertainty.

   3. 3

      Defines an acceptable difference from the low-angle period before judging the model's useful range.

A lightweight footbridge panel is driven by repeated footsteps. Its undamped vibration amplitude peaks at 6.0 mm near 2.0 Hz. Engineers test two add-on dampers at the same forcing amplitude.

1. a

   Interpret Explain why the undamped panel has its greatest response near 2.0 Hz.

   2
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   1. 1

      Identifies 2.0 Hz as close to a natural frequency of the panel.

   2. 2

      Explains that repeated driving near the natural frequency transfers energy effectively, producing resonance and large amplitude.

2. b

   Compare Compare P and Q quantitatively at the resonant frequency.

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   1. 1

      Reads amplitudes 2.8 mm for P and 1.6 mm for Q at 2.0 Hz.

   2. 2

      States that Q reduces amplitude by a further 1.2 mm relative to P, or that Q's amplitude is about 43% lower than P's.

3. c

   Evaluate Recommend a damper for the bridge and specify additional evidence required before installation.

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   1. 1

      Recommends Q if vibration reduction is the main priority, supported by its lower amplitude at all tested frequencies, or gives another defensible conditional recommendation.

   2. 2

      Recognises that measurements at only three frequencies may miss another peak or frequency shift.

   3. 3

      Requests relevant evidence such as a finer frequency sweep, transient response, performance under varied crowd forcing, added mass, fatigue, weather durability, cost, or maintenance.

   4. 4

      Explains how the requested evidence addresses safety, comfort, or whole-life performance rather than merely asking for more data.