Beats

Analyse qualitatively and quantitatively the relationships of the wave nature of sound to explain:

• beats 𝑓_beat = |𝑓₂ − 𝑓₁ |
• The Doppler effect 𝑓′ = 𝑓 (𝑣_wave+𝑣_observer) / (𝑣_wave−𝑣_source)

Learn.

Beats are the result of two waves of similar frequency interfering with one another. The resultant super position creates patches of constructive interference and patches of deconstructive interference, as a result a wah wah wah sound can be heard.

Beats can be explained by the following formula:

•  𝑓_beat = |𝑓₂ − 𝑓₁ |
  • 𝑓_beat = The observed beats due to the super position of similar 𝑓 waves (Hz)
  • 𝑓₂ = either of the two frequencies which are super positioning (Hz)
  • 𝑓₁ = either of the two frequencies which are super positioning (Hz)

Memorise.

Following formula summarizes Beats effect which can be observed as the wah wah when two waves of similar frequency superposition

𝑓_beat = |𝑓₂ − 𝑓₁ |

• 𝑓_beat = The observed beats due to the super position of similar 𝑓 waves (Hz)
• 𝑓₂ = either of the two frequencies which are super positioning (Hz)
• 𝑓₁ = either of the two frequencies which are super positioning (Hz)

Master.

Question 1.

Explain beats and what is required for them to occur? [3 marks]

Question 2.

Two sounds are observed when two guitar strings are played at the same time, the frequency of one wave is 200 Hz and the other is 204 HZ. What is the resultant beats frequency which would be heard? [1 mark]

Question 3.

Could beats be observed if a train is travelling forward emitting a frequency of sound, the sound travels and rebound off a stationary wall. The observer can hear the reflected sound and the original sound – would they notice beats? Justify your answer [4 marks]