PHY C15: Measuring the Speed of Sound using Stationary Waves

Today’s topic:

  • Measuring the speed of sound using stationary waves
    • Procedure
    • End-correction

Let’s go!

How do you measure the speed of sound using stationary waves?
Recall this formula for an air column:

To calculate the speed v of a stationary wave, you can fix the frequency & find the shortest length L able to support the standing wave (where n=1).


What you need:

  • A column with variable length L (done with water)
  • A sound source with a known frequency f (tuning fork)

The set-up:

The procedure:

1. Starting with L = 0, vibrate a tuning fork of known frequency f just above the open end of the tubeThis image has an empty alt attribute; its file name is ccyl3.gif 
2. Increase the length L (by lowering the water level or raising the tube) until the first loud noise is heardThis length L1 is the length required to support the 1st harmonic of frequency f

It can be concluded that:
L1 + e = λ/4

The term e is the additional length due to end-correction* (see below)
4. Repeat the procedure, increasing the length L until a second loud noise is heardThis length L2 is the length required to support the 2nd harmonic of frequency f

It can be concluded that:
L2 + e = 3λ/4
5. Eliminate end-correctionSubtract the 2 equations:
(L2 + e) – (L1 + e) = (3λ/4) – (λ/4)

L2 – L1 = 2λ/4

L2 – L1 = λ/2
6. Calculate vUsing v = fλ,

L2 – L1 = v/2f

v = 2f(L2 – L1)

*What is End-Correction?
The difference in length between the tube & the actual air column.

Since the sound source will be slightly above the tube, the actual distance L is slightly longer than the measured length of the tube.

Thus, the antinode of the stationary at the open end is actually slightly outside the tube.

This difference in length is denoted by e.

How do we get rid of this difference?
By repeating the procedure at least twice & subtracting the equations (as you can see above).

⇐ Previous in Physics: Stationary Waves in Strings/Air Columns
⇒ Next in Physics: Double Slit Interference

3 thoughts on “PHY C15: Measuring the Speed of Sound using Stationary Waves

  1. Pingback: PHY C15: Stationary Waves in Strings/Air Columns – ProDuckThieves

  2. Pingback: 15. Superposition – ProDuckThieves

  3. Pingback: PHY C15: Double Slit Interference – ProDuckThieves

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