Question

A bugle can be thought of as an open pipe. If a bugle were straightened out, it would be 2.65 mlong.a.) If the speed of sound is 343m/????, find the lowest frequency that is resonant for a bugle (ignoring end corrections)b.) Find the next two resonant frequencies for the bugle.

Answer 1

Answer:

(a). The lowest frequency is 64.7 Hz.

(b). The next two resonant frequencies for the bugle are 129.4 Hz and 194.2 hz.

Explanation:

Given that,

Length = 2.65 m

Speed of sound = 343 m

We need to calculate the wavelength

Using formula of wavelength

$\lambda=2l$

Put the value into the formula

$\lambda=2\times2.65$

$\lambda=5.3\ m$

(a). We need to calculate the lowest frequency

Using formula of frequency

$f_{1}=\dfrac{v}{\lambda_{1}}$

Put the value into the formula

$f_{1}=\dfrac{343}{5.3}$

$f_{1}=64.7\ Hz$

(b). We need to calculate the next two resonant frequencies for the bugle

Using formula of resonant frequency

$f_{2}=\dfrac{v}{\lambda_{2}}$

$f_{2}=\dfrac{v}{l}$

Put the value into the formula

$f_{2}=\dfrac{343}{2.65}$

$f_{2}=129.4\ Hz$

For third frequency,

$f_{3}=\dfrac{v}{\lambda_{3}}$

$f_{3}=\dfrac{3v}{2l}$

Put the value into the formula

$f_{3}=\dfrac{3\times343}{2\times2.65}$

$f_{3}=194.2\ Hz$

Hence, (a). The lowest frequency is 64.7 Hz.

(b). The next two resonant frequencies for the bugle are 129.4 Hz and 194.2 hz.