# Problem: An unfingered guitar string is 0.73 m long and is tuned to play E above middle C (330 Hz).(a) How far from the end of this string must the finger be placed to play B above middle C (494 Hz)?___ m(b) What is the wavelength on the string of this 494 Hz wave?___ m(c) What are the frequency and wavelength of the sound wave produced in air at 20

###### FREE Expert Solution

Frequency:

$\overline{){\mathbf{f}}{\mathbf{=}}\frac{\mathbf{n}\mathbf{v}}{\mathbf{2}\mathbf{l}}}$

Wavelength in terms of the length of the string.

$\overline{){\mathbf{\lambda }}{\mathbf{=}}\frac{\mathbf{2}\mathbf{l}}{\mathbf{n}}}$

(a)

From the first equation, the velocity remains constant. The number n also remains constant.

Therefore, we have the ratios:

$\begin{array}{rcl}\frac{{\mathbf{f}}_{\mathbf{0}}}{{\mathbf{f}}_{\mathbf{n}}}& \mathbf{=}& \frac{{\mathbf{l}}_{\mathbf{n}}}{{\mathbf{l}}_{\mathbf{0}}}\\ {\mathbf{l}}_{\mathbf{n}}& \mathbf{=}& \mathbf{\left(}\frac{{\mathbf{f}}_{\mathbf{0}}}{{\mathbf{f}}_{\mathbf{n}}}\mathbf{\right)}{\mathbf{l}}_{\mathbf{0}}\\ & \mathbf{=}& \mathbf{\left(}\frac{\mathbf{330}}{\mathbf{494}}\mathbf{\right)}\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{73}\mathbf{\right)}\end{array}$

87% (37 ratings) ###### Problem Details

An unfingered guitar string is 0.73 m long and is tuned to play E above middle C (330 Hz).

(a) How far from the end of this string must the finger be placed to play B above middle C (494 Hz)?
___ m
(b) What is the wavelength on the string of this 494 Hz wave?
___ m
(c) What are the frequency and wavelength of the sound wave produced in air at 20

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