When you blow across the top of a
soda bottle, it acts like a closed pipe
with a fundamental frequency of
495 Hz. If you pour 0.030 m of water
into the bottle, shortening the air cavity,
what is the new fundamental frequency?
(Hint: Find the original length.)
(Speed of sound = 343 m/s)
(Unit = Hz)

The new fundamental frequency will be 598.7Hz.

Explanation:

The fundamental wavelength of the sound waves in the soda bottle is given by the equation

where is the speed of sound, and is the frequency. Since and , we have

Because it is a fundamental wavelength, the length   of the soda can must be

The length of the soda bottle is 0.173 meters.

Now, if we pour 0.030 m of water, the new length of the air cavity becomes

Therefore, the new fundamental wavelength will be

,

which is a frequency of

Thus, the new fundamental frequency is 598.7Hz.

80cm/s.

24cm/s.

53.3cm/s.