Consider standing waves in a pipe of length l-8.5 m containing a column of air. the speed of sound in the columns is vs 333 m/s. each of the standing wave images provided may represent a case for which one or both ends are open 13% part (a) select the image from the options provided showing the displacement of air particles for the third harmonic of a ?

58.8Hz

Explanation:

Harmonics or overtones are multiple integrals of the fundamental frequencies. Sound waves can occur both in closed pipes, open pipes and strings.

First we need to get the fundamental frequency in open pipes.

Note that frequency = velocity/wavelength

The length of the pipe (L) with fundamental frequency in term of its wavelength is ¶/2 (taking ¶ as wavelength)

L = ¶/2

¶ = 2L

Substituting this in the fundamental frequency formula

Fo = v/¶

Fo = v/2L

Since v = 333m/s

L = 8.5m

Fo = 333/2(8.5)

Fo = 333/17

Fo = 19.6Hz

This fundamental frequency will be the first harmonics

First overtone (f1) will be the second harmonics f1 = 2fo

Second overtone (f2) will then be third harmonics f2 = 3fo

f2 = 3×19.6

F2 = 58.8Hz

Third harmonic frequency will be 58.8Hz

*Check attachment for diagram

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west