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Chapter 2: Q26E (page 539)

The fundamental frequency of a pipe that is open at both ends is 524 Hz. (a) How long is this pipe? If one end is now closed, find (b) the wavelength and (c) the frequency of the new fundamental.

Short Answer

Expert verified

a)the length of the pipe is0.328鈥尘

b) The wavelength is 1.312鈥尘

c) The frequency of new fundamental is 262.2鈥塇锄.

Step by step solution

01

Concept of the frequency of the open and closed pipe.

The frequency of standing wave in an open pipe is f=nv2L and the frequency of standing wave in a closed pipe isf=v位=nv4L where,f is The frequency of nth harmonic, v is the velocity of the wave,n,nth harmonic (n 鈥� 1, 2, 3, ... ) , L is the length of the pipe.

02

Calculate the length of the pipe Fundamental frequency is the first harmonic n=1

L=nv2f1=1脳344鈥嬧�尘/s2脳524鈥塇锄=0.328鈥尘

Therefore, the length of the pipe is 0.328鈥尘.

03

Calculate the wavelength

The wavelength is given as

l=4Ln=4脳0.328鈥尘1=1.312鈥尘

04

Calculate the frequency of new fundamental

The new fundamental frequency is given as

f=nv4L=1脳344鈥尘/s4脳0.328鈥尘=262.2鈥塇锄

The new fundamental frequency and wavelength are262.2鈥塇锄 and 1.312鈥尘respectively.

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