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The fundamental frequency of an open organ pipe corresponds to B above middle C (493.9 Hz on the chromatic musical scale). The third resonance of a different closed organ pipe has the same frequency. What are the lengths of the two pipes? (Assume that the speed of sound in air is 343 m/s.)

1. open pipe
m
2. closed pipe
m

Respuesta :

Answer:

For open end the length of pipe is 0.347 meter.

The length of pipe for closed end is 0.521 meter.

Explanation:

Given

fundamental frequency = f 1 = 493.9 Hz

Velocity of sound= v = 343 m/s

1. For open end pipe the formula for frequency = (n×v)/2×l

v stands for velocity

n represent number of harmonics or resonance

l stands for length of the pipe

                         f 1 = (n×v)/(2×l)

                   we want to find out the length of open end pipe so

                       f 1 × 2×l = n×v

                                  l  = (n×v)/(2×f 1)

                                  l  = (1×343)/(2×493.9)

                                  l  = 343/987.8

                                  l  = 0.347 m

For open end the length of pipe is 0.347 meter.

Part B

For close end pipe the formula for frequency =   f  = (n×v)/(4×l)

                           f  = (n×v)/(4×l)  

               we want to find the length of closed pipe

                           f  × 4×l = n×v

                                  l  = (n×v)/(4×f )

     n=3 for third resonance

frequency will be same as fundamental frequency=f 1=f 3 =  493.9 Hz (given)

                              v= 343 m/s

            l  = (n×v)/(4×f )

Now put the values in above equation

           l  = (3×343)/(4×493.9)

           l  = 1029/1975.6

           l  = 0.521 m    

The length of pipe for closed end is 0.521 meter

                                                                     

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