This is because the pitch of the sound we hear depends on the frequency of the sound wave that can be created within the bottle's air. The shorter the air column that is, the shorter the height of the air in the bottle the higher the frequency. And the higher the frequency the higher the perceived pitch. This is why the empty bottle should have produced a sound wave with a lower frequency than the others and the bottle that was nearly full three quarters full should have made the highest pitch.

In fact, because the air column in the half-full bottle was half the length of the air column in the empty bottle, the half-full bottle should have produced a frequency that was twice the empty bottle's frequency. For more on the mathematics behind this, see the "More to explore" section. Similarly, the three-quarter-full bottle should have produced a frequency that was twice that of the half-full bottle.

When one sound wave is twice the frequency of another, the pitches made are one octave apart. For example, the middle C note on a piano has a frequency of hertz whereas the C that is one octave higher has a frequency of hertz. This means that the half-full bottle should have made a note one octave higher than the empty bottle, and the three-quarter-full bottle should have made a note one octave higher than the half-full one.

This activity brought to you in partnership with Science Buddies. You have free article s left. Already a subscriber? Sign in. See Subscription Options. Sign Up. Materials Three identical narrow-neck bottles They can be glass or plastic. Try blowing across the tops of the bottles you selected to make a resonant sound. Do this by holding the bottle upright so it is perpendicular to your face. Touch your lower lip to the edge of the bottle, pursing your upper lip and blowing gently over the opening.

When you get the angle and airflow just right, you will hear a musical note as the air column in the open bottle resonates. How does the bottle sound?

If you cannot make a note by blowing over the bottles, try using different bottles for this activity. If you've seen these problems, a virtual contest is not for you - solve these problems in the archive. If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive. Never use someone else's code, read the tutorials or communicate with other person during a virtual contest. No tag edit access.

Problems Submit Status Standings Custom test. The problem statement has recently been changed. We may want to round to tens, hundreds, etc, In this case we replace the removed digits with zero. To round to "so many" significant digits, count digits from left to right , and then round off from there. When there are leading zeros such as 0.

Try increasing or decreasing the number of significant digits. Also try numbers with lots of zeros in front of them like 0. Hide Ads About Ads.

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