Closed End Air columns (Finding Sound Velocity)

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Theory:

A musical instrument has a set of natural frequencies at which it vibrates at when a disturbance is introduced into it. These natural frequencies are known as  the harmonics of the instrument. Each harmonic is associated with a standing wave pattern.

Aim: To Investigate the relationship of frequency and Lenght of air column

Problem Solving:
Internalize the mathematical relationships for the closed-end air columns in order to perform calculations predicting the velocity of a sound wave produced by a known length of air column and  given a natural frequencies.

The graphic  below depicts the relationships between the key variables in such calculation.

High amplitude to high amplitude shows in the Visual analyser is = 𝞴/2

𝞴, v, L and f can be relate by the equation  v =f𝞴   where  𝞴=L

Apparatus/ Materials:
speaker, meter tape, one end closed tube  microphone, connecting wires

Software: Visual Analyser

Variables:
Maipulated: Frequency,f      Responding: Wavelength, 𝞴      Constant to find: velocity of s/wave, v

Arrangement of Apparatus:

App. and Software

with co-partner

with an assistance

 Procedure:

1: Experiment done by viewing the amplitude of wavelength in the visual analyser, VA generate wave with desirable frequency 1200 Hz.
2. The microphone is move further from the speaker until the highest peak is shown on the VA screen. that is  𝞴/2. More further more until one more highest peak is shown on the VA screen and marked the distance as 𝞴.
3. Repeat Step 1 and 2 with different frequecy 1400 hz, 1600 Hz, 1800 Hz and 2000 Hz.
4. Tabulate data
5. Plot graph of f against 1/𝞴

Tabulation of data:

Analysis from graph:

  Calculation:
  Gradient of the graph =  1400 - 1200 / 0.0417 - 0.0357
                                     =  200 / 0.006
                                     =  33333.33cms-1
                                     =  333 ms-1

Since v = f𝞴
          f = (1/𝞴) v
          f ∝ 1/𝞴    graph plotted ⏫

Conclusion:

• The graph of  f against 1/𝞴  is equal to Velocity Of Sound Wave
•  Velcity of Sound Wave, v = 333ms-1

Visualising on the VA:

Authentic Link: