To measure the velocity of sound in air by means of a resonance tube

We saw on page 315 that the velocity of sound is given by the formula

and hence if we can find the wavelength, A, of the sound wave emitted by a standard tuning fork of frequency, f, we may easily calculate the velocity, v.

The resonance tube suggests a method of doing this. In the first position of
resonance the length of the tube is A/4, and therefore it would appear that A can be found by multiplying the tube length by 4. However, there is a difficulty. The antinode at the top does not coincide exactly with the top of the tube, but projects slightly above it by an amount which is called the end correction, c. Fortunately the difficulty may be overcome by measuring the length of the tube for the second position of resonance as well as the first (see Fig. 29.8). By subtracting one from the other, the end correction is eliminated and we obtain a correct value for half a wavelength.

Thus, if length of tube for 1st position of resonance = II
and length of tube for 2nd position of resonance = 12

Either of the forms of apparatus shown in Fig. 29.6 are suitable for the above experiment. Fig. 29.9 illustrates a method for measuring the length of the air column which helps to overcome errors caused by the meniscus of the water.

A bent wire is inserted into a small hole drilled in the end of a boxwood scale. A reading of the top of the tube against the scale is taken when the tip of the bent wire is just level with the water surface. The distance, x, is afterwards measured and added to this reading in order to obtain the correct length I, or 12,