All Solutions
Page 419: Section Review
$textit{b.}$, Sound of clarinet is produced by reeds.
$textit{c.}$, Sound of tuba is produced by the lips of the player.
$textit{d.}$, Sound of violin is produced by string.
$textit{b.}$ reeds
$textit{c.}$ lips of the player
$textit{d.}$, string
The longer the tube is the lower resonant frequency will be.
$f_{1} = 370, mathrm{Hz}$
$f_{2}$ , $f_{3}$, $f_{4}$ $= ?$
Harmonics are given by the product of a whole number and fundamental ($f_{1}$):
$$
f_{2} = 2 f_{1}
$$
$$
f_{3} = 3 f_{1}
$$
$$
f_{4} = 4 f_{1}
$$
When we put known values into the previous equations:
$$
f_{2} = 2 cdot 370, mathrm{Hz}
$$
$$
boxed{f_{2} = 740, mathrm{Hz}}
$$
$$
f_{3} = 3 cdot 370, mathrm{Hz}
$$
$$
boxed{f_{3} = 1100, mathrm{Hz}}
$$
$$
f_{4} = 4 cdot 370, mathrm{Hz}
$$
$$
boxed{f_{4} = 1480, mathrm{Hz}}
$$
f_{2} = 740, mathrm{Hz}
$$
$$
f_{3} = 1110, mathrm{Hz}
$$
$$
f_{4} = 1480, mathrm{Hz}
$$
Given a frequency of the F sharp note on a violin:
$$
begin{align*}
f_1 = 370 ,mathrm{Hz}
end{align*}
$$
$$
begin{align*}
f_2 &= 2f_1 \
&= 2(370 ,mathrm{Hz})\
&= boxed{740 ,mathrm{Hz}}\
f_3 &= 3f_1 \
&= 3(370 ,mathrm{Hz})\
&= boxed{1110 ,mathrm{Hz}}\
f_4 &= 4f_1 \
&= 4(370 ,mathrm{Hz})\
&= boxed{1480 ,mathrm{Hz}}
end{align*}
$$
$f_3 = 1110 ,mathrm{Hz}$
$$
f_4 = 1480 ,mathrm{Hz}
$$
$L = 2.40, mathrm{m}$
$textit{a.}$, $f = ?$
Frequency is given by:
$$
f = dfrac{v}{lambda}
$$
Therefore, we need to determine wavelength since the speed of sound is known $v = 343, mathrm{m/s}$:
$$
begin{align*}
lambda &= 4L\
&= 4 cdot 4.20, mathrm{m}\
&= 9.60, mathrm{m}\
end{align*}
$$
Frequency will, finally, be:
$$
f = dfrac{343, mathrm{m/s}}{9.60, mathrm{m}}
$$
$$
boxed{f = 35/7, mathrm{Hz}}
$$
$f _{2} = 1.40, mathrm{Hz}$
First we need to determine frequency, and since both pipes are played at the same time, it will now be:
$$
f ‘= f – f_{2}
$$
When we put known values into the previous equation we get:
$$
f = 35.7, mathrm{Hz} – 1.40, mathrm{Hz} = 34.3, mathrm{Hz}
$$
Since length is given by:
$$
L’ = dfrac{lambda}{4}
$$
We have to determine wavelength first:
$$
lambda = dfrac{v}{f}
$$
When we put known values into the previous equation we get:
$$
lambda = dfrac{343, mathrm{m/s}}{34.3, mathrm{Hz}} = 10, mathrm{m}
$$
Finally:
$$
L = dfrac{10}{4}
$$
$$
boxed{L’ = 2.50, mathrm{m}}
$$
Therefore difference will be:
$$
L – L’ = 2.50, mathrm{m} – 2.40, mathrm{m} = boxed{0.10, mathrm{m}}
$$
$textit{b.}$, $0.10, mathrm{m}$
Therefore the frequency of the other fork is either :
$$
392-3 = 389hspace{10mm}text{or}hspace{10mm}392+3 = 395
$$
text{color{#4257b2}Frequency of the other fork is either 389 Hz or 395 Hz}
$$