# Organ pipe A, with both ends open, has a fundamental frequency of 475 Hz. The third harmonic of organ pipe B, with one end open, has the sam

Question

Organ pipe A, with both ends open, has a fundamental frequency of 475 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. Use 343 m/s for the speed of sound in air. How long are (a) pipe A and (b) pipe B?

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1 year 2021-09-01T20:49:12+00:00 1 Answers 9 views 0

The length of organ pipe A is $$L = 0.3611 \ m$$

The length of organ pipe B is  $$L_b = 0.2708 \ m$$

Explanation:

From the question we are told that

The fundamental frequency is  $$f = 475 Hz$$

The speed of sound is  $$v_s = 343 \ m/s$$

The fundamental frequency of the organ pipe A  is mathematically represented as

$$f= \frac{v_s}{2 L}$$

Where L is the length of  organ pipe

Now  making L the subject

$$L = \frac{v_s}{2f}$$

substituting values

$$L = \frac{343}{2 *475}$$

$$L = 0.3611 \ m$$

The second harmonic frequency of the  organ pipe A is mathematically represented as

$$f_2 = \frac{v_2}{L}$$

The third harmonic frequency of the  organ pipe B is mathematically represented as

$$f_3 = \frac{3 v_s}{4 L_b }$$

So from the question

$$f_2 = f_3$$

So

$$\frac{v_2}{L} = \frac{3 v_s}{4 L_b }$$

Making  $$L_b$$ the subject

$$L_b = \frac{3}{4} L$$

substituting values

$$L_b = \frac{3}{4} (0.3611)$$

$$L_b = 0.2708 \ m$$