Question

If you blow across the open end of a soda bottle and produce a toneof 290 Hz, what will be the frequency of the next harmonic heard ifyou blow much harder? (Hz)

Answer 1

f = 96.56 Hz

Step-by-step explanation:

A soda bottle can be simulated by a system of a tube with one end open and the other closed. In this case at the closed end we have a node and at the open end a maximum, so the wavelength is

λ = 4L / n

where n = 1, 3, 5, ...

for our case the speed of sound is

v = λ f

we substitute

f / v = 4L / n

calculate

290 / (340 4) = L / n

0.213 = L / n

In the exercise the value of n is not indicated, but we can assume that it is the fundamental answer, therefore n = 1

L = 0.213 m

now we can calculate the frequency of the following resonance n = 3

f = 4L v / n

f = 4 0.213 340/3

f = 96.56 Hz