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General Wave Properties: Question 7

Syllabus 3.1

Structured Core 5 marks

A construction site sounds a warning siren before each scheduled blast. An observer stationed 680 m680\text{ m} away sees the flash of the warning light (which arrives essentially instantly) and starts a stopwatch, stopping it the moment the sound of the siren reaches her. The stopwatch reads 2.0 s2.0\text{ s}.

(a) Calculate the speed of the sound wave as it travels from the siren to the observer. [2]

(b) The siren is stated by its manufacturer to produce sound at a frequency of 200 Hz200\text{ Hz}. Using your answer to part (a), calculate the wavelength of the sound wave. [2]

(c) State whether the sound wave travelling through the air is transverse or longitudinal, and justify your answer in terms of the direction air particles vibrate compared with the direction the wave travels. [1]

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Worked solution

Part (a): Calculating the speed of the sound wave

Speed is the distance travelled divided by the time taken. The sound wave travels the 680 m680\text{ m} from the siren to the observer in 2.0 s2.0\text{ s}:

v=distancetime=680 m2.0 sv = \frac{\text{distance}}{\text{time}} = \frac{680\text{ m}}{2.0\text{ s}}

v=340 m/sv = 340\text{ m/s}

Part (b): Calculating the wavelength

The wave equation links speed, frequency and wavelength:

v=fλv = f\lambda

Rearranging for wavelength:

λ=vf\lambda = \frac{v}{f}

Substituting the speed found in part (a) and the manufacturer’s stated frequency of 200 Hz200\text{ Hz}:

λ=340 m/s200 Hz\lambda = \frac{340\text{ m/s}}{200\text{ Hz}}

λ=1.7 m\lambda = 1.7\text{ m}

Part (c): Classifying the sound wave

Sound travels through air as a series of compressions and rarefactions. The air particles vibrate back and forth along the same direction that the wave itself travels, not perpendicular to it.

Since the vibration is parallel to the direction of travel, the sound wave is longitudinal.

Final answers

  • (a) Speed of the sound wave =340 m/s= \boxed{340\text{ m/s}}
  • (b) Wavelength of the sound wave =1.7 m= \boxed{1.7\text{ m}}
  • (c) Longitudinal, air particles vibrate parallel to the direction the wave travels, producing compressions and rarefactions