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PHYSICS, M3 2018 VCE 11

Figure 13 shows two speakers, \(\text{A}\) and \(\text{ B}\), facing each other. The speakers are connected to the same signal generator/amplifier and the speakers are simultaneously producing the same 340 Hz sound.
 

Take the speed of sound to be 340 ms\( ^{-1}\).

  1. Calculate the wavelength of the sound.  (1 mark)

  2. A student stands in the centre, equidistant from speakers \(\text{A}\) and \(\text{B}\). He then moves towards speaker \(\text{B}\) and experiences a sequence of loud and quiet regions. He stops at the second region of quietness.
  3. How far has the student moved from the centre? Explain your reasoning.  (3 marks)

Show Answers Only

a.     \(\lambda=1\ \text{m}\)

b.    → At the centre of the speakers, there is an area of relative loudness

→ This is due to a path difference of 0 metres between the wavelengths of sounds coming from both speaker \(\text{A}\) and speaker \(\text{B}\). 

→ As the student moves towards speaker \(\text{B}\), the two sound waves will experience constructive (loud) and destructive interference (quiet).

→ The peak of speaker \(\text{A}\) will move into the trough of speaker \(\text{B}\) where he experiences the first region of quietness (node) which is 1 quarter wavelength (0.25m) from the centre.

→ The second region of quietness (node) will be half of a wavelength (0.5m) from the first region of quietness. Thus, the total distance from the centre to the second region of quietness is 0.75m.

Show Worked Solution

a.    \(\lambda=\dfrac{v}{f}=\dfrac{340}{340}=1\ \text{m}\)

 

b.    → At the centre of the speakers, there is an area of relative loudness

→ This is due to a path difference of 0 metres between the wavelengths of sounds coming from both speaker \(\text{A}\) and speaker \(\text{B}\). 

→ As the student moves towards speaker \(\text{B}\), the two sound waves will experience constructive and destructive interference.

→ The peak of speaker \(\text{A}\) will move into the trough of speaker \(\text{B}\) where he experiences the first region of quietness (node) which is 1 quarter wavelength (0.25m) from the centre.

→ The second region of quietness (node) will be half of a wavelength (0.5m) from the first region of quietness. Thus, the total distance from the centre to the second region of quietness is 0.75m.

♦♦♦ Mean mark (b) 20%.