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Chapter 2: Q31E (page 540)

You blow across the open mouth of an empty test tube and produce the fundamental standing wave of the air column inside the test tube. The speed of sound in air is 344 m/s and the test tube act as a stopped pipe. (a) If the length of the air column in the test tube is 14.0 cm, what is the frequency of this standing wave? (b) What is the frequency of the fundamental standing wave in the air column if the test tube is half filled with water?

Short Answer

Expert verified
  1. The frequency of the fundamental standing wave in the air is 614 Hz.
  2. If the test tube is half filled with water, the frequency of the fundamental standing wave is 1229 Hz.

Step by step solution

01

STEP 1 Concept of the length of the air column and the frequency of standing wave

The length of the air column is given as L=λ4 and the frequency of standing wave is given as f=vλ where λis the wavelength of the wave.

02

Calculate the frequency when the length is 14.0cm

The length of the closed pipe is 14.0​ cm.The frequency is given by f=vλ.

l4=λl=4λ=4×0.14 m=0.56 m

f=vlf=344 m/s×0.56 m=614 Hz

Therefore, the frequency of the fundamental standing wave in the air is 614 Hz.

03

Calculate the frequency when the length is half filled

The length of the closed pipe is 7.0 cm.

λ=4×0.07 m=0.28 mf=344 m/s×0.28 m=1229 Hz

Therefore, the frequency of the fundamental standing wave in the air column if the test tube is half filled with water is 1229 Hz.

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