Find the length (in m) of an organ pipe closed at one end that produces a fundamental frequency of 494 Hz when air temperature is 18.0°C.

0.173 m.

Explanation:

The fundamental frequency of a closed pipe is given as

fc = v/4l ... Equation 1

Where fc = fundamental frequency of a closed pipe, v = speed of sound l = length of the pipe.

Making l the subject of the equation,

l = v/4fc ... Equation 2

also

v = 331.5*0.6T ... Equation 3

Where T = temperature in °C, T = 18.0 °c

Substitute into equation 3

v = 331.5+0.6 (18)

v = 331.5+10.8

v = 342.3 m/s.

Also given: fc = 494 Hz,

Substitute into equation 2

l = 342.3 / (4*494)

l = 342.3/1976

l = 0.173 m.

Hence the length of the organ pipe = 0.173 m.