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xeze [42]
3 years ago
9

Two open organ pipes, sounding together, produce a beat frequency of 8.0 Hz . The shorter one is 2.08 m long. How long is the ot

her pipe?
Physics
1 answer:
s344n2d4d5 [400]3 years ago
6 0

Answer:

The length of the longer pipe is L = 2.30 m

Explanation:

Given that:

Two open organ pipes, sounding together, produce a beat frequency of 8.0 Hz . The shorter one is 2.08 m long.

How long is the other pipe?

From above;

The formula for the frequency of open ended pipes can be expressed as:

f = \dfrac{nv}{2L}

where n = 1 ( since half wavelength exist between those two pipes)

v = 343 m/s  and L = 2.08 m

Thus, the shorter pipe produces a frequency of :

f = \dfrac{1*343}{2*2.08}

f = \dfrac{343}{4.16}

f =82.45 \ Hz

Also; we know that the beat frequency was given as 8.0 Hz

Then,

The lower frequency of the longer pipe = ( 82.45 - 8.0 )Hz

The lower frequency of the longer pipe = 74.45 Hz

Finally;

From the above equation; make Length L the subject of the formula. Then,

The length of the longer pipe is L = \dfrac{nv}{2f}

The length of the longer pipe is L = \dfrac{1*343}{2*74.45}

The length of the longer pipe is L = \dfrac{343}{148.9}

The length of the longer pipe is L = 2.30 m

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Complete Question

The diagram for this question is shown on the first uploaded image

Answer:

The distance traveled in horizontal direction is D = 1.38 m

Explanation:

From the question we are told that

      The length of the string is  L = 1.6 \ m

      The mass of the ball is  m = 200 g = \frac{200}{1000} = 0.2 \ kg

       The height of ball is  h = 1.5 \ m

Generally the work energy theorem can be mathematically represented as

               PE = KE

   Where PE is the loss in potential energy which is mathematically represented as

                   PE =mgh

Where h is the difference height of ball at A and at B  which is mathematically represented as

                 h = y_A - y_B

So        PE =mg(y_A - y_B)              

While KE is the gain in kinetic energy which is mathematically represented as

               KE   = \frac{1}{2 } (v_b ^2 - 0)

Where v_b is the velocity of the of the ball

  Therefore we have from above that

                    PE =KE \equiv mg (y_A - y_B) = \frac{1}{2} m (v_b ^2 - 0)

               Making v_b the  subject we have

      v_b = \sqrt{2g (y_A - y_B)}

substituting values

      v_b = \sqrt{2g (1.5 - 0.40)}

     v_b = 4.6 \ m/s

Considering velocity of the ball when it hits the  floor in terms of its vertical and horizontal component we have

         v_x = 4.6 m/s \ while \ v_y = 0 m/s

The time taken to travel  vertically from the point the ball broke loose  can be obtained using the equation of motion

            s = v_y t - \frac{1}{2} g t^2

Where s is distance traveled vertically which given in the diagram as s = -0.4

The negative sign is because it is moving downward

     Substituting values

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         solving for t we have  

               t = 0.3 \ sec

Now the distance traveled on the horizontal is mathematically evaluated as

           D =  v_b * t

           D =  4.6 * 0.3

           D = 1.38 m

8 0
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