A standing wave in a column of air with both ends open has a frequency of 520 Hz.The next higher harmonic has a frequency of 780 Hz.How long is the column of air?
A)33.8 cm
B)45.1 cm
C)66.0 cm
D)86.8 cm
E)92.3 cm

Question

Quizplus · Accepted Answer

For a column of air with both ends open, the wavelength of the standing wave (λ) is equal to twice the length of the column (L).

The frequency of the first harmonic (fundamental frequency) is given by:

f1 = v/2L

where v is the speed of sound in air.

The frequency of the second harmonic (first overtone) is given by:

f2 = 3v/2L

We are given that f1 = 520 Hz and f2 = 780 Hz.

Dividing the second equation by the first equation, we get:

f2/f1 = (3v/2L)/(v/2L) = 3/2

Solving for L, we get:

L = v/(2(f2/f1 - 1))

Plugging in the given values, we get:

L = 343 m/s / (2(780/520 - 1)) = 0.66 m = 66.0 cm

Therefore, the length of the column of air is 66.0 cm.

A Standing Wave in a Column of Air with Both