Question

If you blow across the open end of a soda bottle and produce a tone of 250 Hz, what will be the frequency of the next harmonic heard if you blow much harder?

___Hz

Answer 1

Answer:

Generally, the lowest overtone for a pipe open at one end and closed would be at  y / 4  where y represents lambda, the wavelength.

Since F (frequency) = c / y       Speed/wavelength

F2 / F1 = y1 / y2      because c is the same in both cases

F2 = y1/y2 * F1

F2 = 3 F1 = 750 /sec

Note that L = y1 / 4 = 3 y2 / 4 for these wavelengths to fit in the pipe

and y1 = 3 y2

Answer 2

The second harmonic will be three times the first harmonic. The answer is 750 Hz

VIBRATION OF WAVES IN PIPES

Closed pipes have odd multiples of frequencies or harmonics. That is,

If  $F_{0}$ = fundamental frequency = first harmonic

$F_{1}$ = 3$F_{0}$ = second harmonic

$F_{2}$ = 5$F_{0}$ = third harmonic

$F_{3}$ = 7$F_{0}$ = fourth harmonic

Let assume that the first harmonic is 250 Hz, If you blow it much harder, second, third or fourth harmonic can be produced.

By using the formula above,

second harmonic will be 3 x 250 = 750Hz

Therefore, the frequency of the next harmonic heard if you blow much harder will be 750 Hz

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