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3 years ago

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How long must a flute be in order to have a fundamental frequency of 262 Hz (this frequency corresponds to middle C on the evenl

y tempered chromatic scale) on a day when air temperature is 20.0°C ? It is open at both ends.

1 answer:

spin [16.1K]3 years ago

7 0

Answer:

L=0.654 m

Explanation:

<u>Concepts and Principles </u>

1- The speed of sound in air is expressed as a function of the temperature of air as follows:

v=(331 m/s)√(1+T_C/273°C) (1)

where 331 m/s is the speed of sound in air at temperature 0°C and Tc is the temperature of air in Celsius.

<u>Standing Wave Patterns in Pipes: </u>

A pipe open at both ends can have standing wave patterns with resonant frequencies:

f=v/λ=nv/2L n=1,2,3.........

where v is the speed of sound in air.

<u>Given Data </u>

f_1 (fundamental frequency of the flute) = 262 Hz

T (temperature of the air) = 20°C

The flute is open at both ends.

<u>Required Data </u>

We are asked to determine the length of the tube.

<u>Solution</u><u> </u>

The speed of sound in air at temperature T = 20°C is found from Equation (1):

v=(331 m/s)√(1+T_C/273°C)

=342.91 m/s

The fundamental frequency of the flute is found by substituting n = 1 into Equation (2):

f=v/2L

Solve for L:

L=v/2f_1

L=0.654 m

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