Question

If the fundamental frequency of a cylinder is 310 Hz, and the speed of sound is 343 m/s, determine the length of the cylinder (in m) for each of the following cases.

a. the cylinder is closed at one end
b. the cylinder is open at both ends.

Answer 1

a)
`l=0.276m`

b)
`l'=1.11m`

Step-by-step explanation:

From the question we are told that:

Frequency
`F=310Hz`

Speed
`V=343m/s`

a)

Generally the equation for Frequency is mathematically given by

The cylinder is closed at one end

`F=(V)/(4*l)`

`310=(343)/(4*l)`

`l=0.276m`

b)

Generally the equation for Frequency is mathematically given by

the cylinder is open at both ends.

`F=(V)/(l')`

`310=(343)/(l')`

`l'=1.11m`

Answer 2

(a) 0.277 m

(b) 0.553 m

Step-by-step explanation:

(a) For the closed cylinder,

Applying,

f' = v/4l............. Equation 1

Where f' = fundamental frequency, v = velocity of sound, l = lenght of the cylinder

make l the subject of the equation

l = v/4f'............. Equation 2

From the question,

Given: v = 343 m/s, f' = 310 Hz

Substitute these values into equation 2

l = 343/(4×310)

l = 0.277 m

(b) For the open cylinder,

f' = v/2l

l = v/2f'................ Equation 3

Substitute into equation 3

l = 343/(2×310)

l = 0.553 m