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Chapter 2: Q29E (page 540)

The longest pipe found in most medium-size pipe organs is 4.88 m (16 ft) long. What is the frequency of the note corresponding to the fundamental mode if the pipe is (a) open at both ends, (b) open at one end and closed at the other?

Short Answer

Expert verified

a) The frequency of the standing wave in an open pipe is 35.25鈥塇锄

b) The frequency of the standing wave in a pipe closed at one end is 17.623鈥塇锄

Step by step solution

01

Step 1 Concept of the frequency of standing wave in an open pipe and closed pipe

Thefrequency of the standing wave in an open pipe is given asf=nv2Land thefrequency of the standing wave in a closed pipe isf=nv4Lwhere,f is the frequency of nth harmonic, v is the velocity of the wave,n representsnthharmonic (n 鈥� 1, 3, 5, ...), L is the length of the pipe.

02

Calculation of the frequency in an pipe

The frequency of standing wave in an open pipe is given as

f1=nv2L=1脳344鈥尘/s2脳4.88鈥尘=35.25鈥塇锄

The frequency of standing wave in a pipe closed at one end is given as

f1=nv4L=1脳344鈥尘/s4脳4.88鈥尘=17.623鈥塇锄

The frequencies are35.25鈥塇锄 and17.623鈥塇锄 respectively.

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