91影视

For an open tube open tube with length \(l\) , the fundamental frequency is \(f = \frac{v}{{2l}}\). Here, \(v = 5000\;{\rm{m/s}}\)is the speed of sound in the metal.

The length of the room is \(l = 80\;{\rm{cm}} = 80\;{\rm{cm}} \times \frac{{1\;{\rm{m}}}}{{100\;{\rm{cm}}}} = 0.80\;{\rm{m}}\).

Part (a)

The frequency of the fundamental tone for the length is,

\(\begin{array}{c}f = \frac{v}{{2l}}\\f = \frac{{5000\,{\rm{m/s}}}}{{2\left( {0.80\,{\rm{m}}} \right)}}\\f \approx 3187.5\,{\rm{Hz}}\end{array}\)

Hence the fundamental frequency is \(3187.5\,{\rm{Hz}}\).

Part (b)

The wavelength of sound in the rod is two times its length which is,

\(\begin{array}{c}\lambda = 2 \times 0.8\;{\rm{m}}\\ = {\rm{1}}{\rm{.6}}\,{\rm{m}}\end{array}\)

Hence, the wavelength is \({\rm{1}}{\rm{.6}}\,{\rm{m}}\).

Part (c)

The frequency and speed of sound in air determine the wavelength of the sound in air.

\(\begin{array}{c}\lambda ' = \frac{v}{f}\\ = \frac{{343\,{\rm{m/s}}}}{{3187.5\,{\rm{Hz}}}}\\ \approx 0.1076\,{\rm{m}}\end{array}\)

Hence, the traveling wavelength of the sound in air is \(0.1076\,{\rm{m}}\).