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Chapter 17: Q46PE (page 630)

What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

Short Answer

Expert verified

The length of the tube is 1.56 m.

Step by step solution

01

Given Data

The fundamental frequency is110 Hz.

The speed of the sound is v = 343 ms/s.

02

Calculation of the length of the tube 

The resonance frequencies of a tube open at both the ends are,

\({{\rm{f}}_{\rm{n}}}{\rm{ = n}}\frac{{\rm{v}}}{{{\rm{2l}}}}{\rm{,}}\;{\rm{n = 1,2,}}\;{\rm{3,}}\;...\)

The fundamental frequency is

\(\begin{aligned}{\rm{110 = }}\frac{{{\rm{343}}}}{{{\rm{2l}}}}\\{\rm{l = }}\frac{{{\rm{343}}}}{{{\rm{2 \times 110}}}}\\{\rm{ = 1}}{\rm{.56}}\;{\rm{m}}{\rm{.}}\end{aligned}\)

Hence, the length of the tube is 1.56 m

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