An empty bottle of height 0.2 m and a second empty bottle of height 0.4 m are placed next
to each other. One person blows into the tall bottle and one blows into the shorter bottle.
What is the difference in the pitch of the two sounds? What could you do to make them
sound at the same pitch?Sound comes out of bottles when you blow on them because your breath creates a series
of standing waves inside the bottle. The pitch of the sound is inversely proportional to the
wavelength, according to the equation. We know that the wavelength is directly
proportional to the length of the standing wave: the longer the standing wave, the greater
the wavelength and the lower the frequency. The tall bottle is twice as long as the short
bottle, so it vibrates at twice the wavelength and one-half the frequency of the shorter
bottle. To make both bottles sound at the same pitch, you would have to alter the
wavelength inside the bottles to produce the same frequency. If the tall bottle were half-
filled with water, the wavelength of the standing wave would decrease to the same as the
small bottle, producing the same pitch.
Pitch of Stringed Instruments
When violinists draw their bows across a string, they do not force the string to oscillate at
any particular frequency, the way the mass on a spring does. The friction between the
bow and the string simply draws the string out of its equilibrium position, and this causes
standing waves at all the different wavelengths in the harmonic series. To determine what
pitches a violin string of a given length can produce, we must find the frequencies
corresponding to these standing waves. Recalling the two equations we know for the wave
speed, and , we can solve for the frequency, , for any term, n, in the
harmonic series. A higher frequency means a higher pitch.
You won’t need to memorize this equation, but you should understand the gist of it. This
equation tells you that a higher frequency is produced by (1) a taut string, (2) a string
with low mass density, and (3) a string with a short wavelength. Anyone who plays a
stringed instrument knows this instinctively. If you tighten a string, the pitch goes up (1);
the strings that play higher pitches are much thinner than the fat strings for low notes
(2); and by placing your finger on a string somewhere along the neck of the instrument,
you shorten the wavelength and raise the pitch (3).