ChemPhys 173/273

Unit 4: Sound and Music

Problem Set C

 

Overview:

Problem Set C targets your ability to analyze physical situations involving resonating air columns - both open-end and closed-end. There are a variety of skills and conceptual understandings required to be successful in such analyses. Such skills and conceptual understandings include the following:

 

 

 

 

 

v = f •
where v represents the speed (or velocity) of the wave, f represents the frequency of the wave, and represents the wavelength of the wave. As mentioned above, the speed of a sound wave in air is dependent upon the air temperature and not upon the properties of the wave. Thus, alterations in the frequency for a wave in a non-changing medium result in inverse alterations in the wavelength with no change in wave speed.

 

 

fn = n • f1
where fn is the frequency of a harmonic, n is the harmonic number associated with that harmonic and f1 is the frequency of the first harmonic or the fundamental frequency.

 

 

 

 

 

Additional Readings/Study Aids:

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in mathematical analysis of resonating air columns.

 Speed of Sound | Standing Wave Patterns | Harmonics

Open-end Air Columns | Closed-end Air Columns | Beats and Beat Frequency

 

View Sample Problem Set.

 

Problem

Description

Audio Link
1

Determination of the length of an closed-end air column from knowledge of the frequency and the speed of sound.

2

Determination of the speed of sound from the frequency and the length of an open-end air column.

3

Determination of the length of an open-end air column from knowledge of the frequency and the speed of sound.

4

Determination of the length of a closed-end air column from knowledge of the frequency and the speed of sound.

5

Determination of the frequency of a harmonic from knowledge of the length of a closed-end air column and the speed of sound.

6

Determination of the length of an open-end air column from knowledge of the frequency and the temperature (which effects wave speed).

7

Referring to the previous problem; determination of the length of an open-end air column from knowledge of the frequency and the temperature (which effects wave speed).

8

Complex analysis involving the determination of the third resonant length of a closed-end air column if given the first and the second resonant length.

9

Referring to the previous problem; determination of the frequency of the tuning fork which forces such an air column into resonance.

10

Determination of the fundamental frequency of an open-end air column with knowledge of the length of the column and the speed of sound.

11

Referring to the previous problem; determination of the second harmonic frequency of a second column which is longer than the previous column by a specified factor.

12

A complex analysis involving the comparison of an open- and a closed-end air column of varying lengths.

13

Determination of the fundamental frequency of a room of air of known length and air temperature (from which the wave speed can be determined).

14

Determination of the length of a closed-end air column from knowledge of the frequency and the speed of sound.

15

Referring to the previous problem; comparison of the above closed-end column to an open-end column of a different length. Requires good thinking skills.

16

Determination of the frequency of a harmonic from knowledge of the length of a closed-end air column and the speed of sound.

17

A complex analysis involving the comparison of an open- and a closed-end air column of the same length. Requires good thinking skills.

18

Referring to the previous problem; determination of the frequency of a higher harmonic from knowledge of the fundamental frequency.

19

A complex analysis involving the use of the beat frequency to determine the length of a violin string from knowledge of the length of another string which has a slightly different frequency.

20

A complex analysis involving the comparison of a closed-end air column and a guitar string of a different length. Requires good thinking skills

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