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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.

User Adam Dziendziel
by
2.8k points

2 Answers

18 votes
18 votes

Answer:

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

User Bethania
by
2.9k points
13 votes
13 votes

Answer:

(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

User Cliff Burton
by
2.9k points