StoryTimStoryTim

ee Nikola Tesla, one of the inventors of radioNikola Tesla, one of the inventors of radio

& an archetypical & an archetypical mad scientistmad scientist, told a , told a

reporter the following story about an application of resonance. reporter the following story about an application of resonance.

He built an electric vibrator that fit in his pocket, & attached it to one of the He built an electric vibrator that fit in his pocket, & attached it to one of the steel beams of a building that was under construction in New York. Although steel beams of a building that was under construction in New York. Although the article didn’t say so, he presumably claimed to have tuned it to the the article didn’t say so, he presumably claimed to have tuned it to the resonant frequency of the building. “resonant frequency of the building. “In a few minutes, I could feel the In a few minutes, I could feel the beam trembling. Gradually the trembling increased in intensity beam trembling. Gradually the trembling increased in intensity and extended throughout the whole great mass of steel. Finally, and extended throughout the whole great mass of steel. Finally, the structure began to creak & weave, & the steelworkers came the structure began to creak & weave, & the steelworkers came to the ground panic-stricken, believing that thereto the ground panic-stricken, believing that there

had been an earthquake. ... [If] I had kept on ten minutes more, I had been an earthquake. ... [If] I had kept on ten minutes more, I couldcould

have laid that building flat in the street.”have laid that building flat in the street.” Is this physically plausible?Is this physically plausible?

Open-end Air ColumnsOpen-end Air Columns

An open air column has a fundamental frequency An open air column has a fundamental frequency of 200 Hz. What is the frequency of the second of 200 Hz. What is the frequency of the second harmonic (first overtone)?harmonic (first overtone)?

A. 300 Hz A. 300 Hz B. 400 Hz B. 400 Hz C. 600 Hz C. 600 Hz D. 800 D. 800 HzHz

If the length of the air column is increased, the If the length of the air column is increased, the frequency of the fundamental is:frequency of the fundamental is:

A. increasedA. increased B. decreasedB. decreased C. the sameC. the same

Open-end Air ColumnsOpen-end Air Columns

An open air column has a fundamental frequency An open air column has a fundamental frequency of 200 Hz. What is the frequency of the second of 200 Hz. What is the frequency of the second harmonic (first overtone)?harmonic (first overtone)?

A. 300 Hz A. 300 Hz B. 400 Hz B. 400 Hz C. 600 Hz C. 600 Hz D. 800 D. 800 HzHz

If the length of the air column is increased, the If the length of the air column is increased, the frequency of the fundamental is:frequency of the fundamental is:

A. increasedA. increased B. decreasedB. decreased C. the sameC. the same

Resonance in Resonance in Closed Air Closed Air ColumnsColumns

3U Physics3U Physics

Resonance in Closed-End Resonance in Closed-End Air ColumnsAir Columns

If one end of an air column If one end of an air column is closed off, it must have is closed off, it must have a node at that end. a node at that end.

The first harmonic of a The first harmonic of a closed-end air column is closed-end air column is therefore:therefore:

Resonance in Closed-End Resonance in Closed-End Air ColumnsAir Columns

If one end of an air column If one end of an air column is closed off, it must have is closed off, it must have a node at that end. a node at that end.

The first harmonic of a The first harmonic of a closed-end air column is closed-end air column is therefore:therefore:

Resonance in Closed-End Resonance in Closed-End Air ColumnsAir Columns

If one end of an air column If one end of an air column is closed off, it must have is closed off, it must have a node at that end. a node at that end.

The first harmonic of a The first harmonic of a closed-end air column is closed-end air column is therefore:therefore:

Note that Note that = 4 = 4LL (or (or LL = = /4)./4).

Higher HarmonicsHigher Harmonics

The next higher harmonic that can be The next higher harmonic that can be produced is:produced is:

Higher HarmonicsHigher Harmonics

The next higher harmonic that can be The next higher harmonic that can be produced is:produced is:

Higher HarmonicsHigher Harmonics

The next higher harmonic that can be The next higher harmonic that can be produced is:produced is:

= 4= 4LL/3 or /3 or LL = = 33/4/4

Higher HarmonicsHigher Harmonics

The next higher harmonic that can be The next higher harmonic that can be produced is:produced is:

= 4= 4LL/3 or /3 or LL = 3 = 3/4 /4

This harmonic is called the 3This harmonic is called the 3rdrd (and not (and not the 2the 2ndnd) harmonic because its frequency ) harmonic because its frequency is 3 times that of the fundamental is 3 times that of the fundamental frequency.frequency.

Higher HarmonicsHigher Harmonics

Similarly, the next higher harmonic is Similarly, the next higher harmonic is the fifth harmonic:the fifth harmonic:

= 4= 4LL/5 or /5 or LL = 5 = 5/4/4

Longitudinal WavesLongitudinal Waves

What do these standing waves actually What do these standing waves actually look like?look like?

Longitudinal WavesLongitudinal Waves

What do these standing waves actually What do these standing waves actually look like?look like?

Closed-End Air Columns Closed-End Air Columns ExampleExample

A closed-end air tube A closed-end air tube resonates to a resonates to a tuning fork of 480 tuning fork of 480 Hz at lengths of 53.0 Hz at lengths of 53.0 cm and 88.5 cm. cm and 88.5 cm. What is the speed of What is the speed of sound in air?sound in air?

Closed-End Air Column Closed-End Air Column ExampleExample

A closed-end air tube A closed-end air tube resonates to a resonates to a tuning fork of 480 tuning fork of 480 Hz at lengths of 53.0 Hz at lengths of 53.0 cm and 88.5 cm. cm and 88.5 cm. What is the speed of What is the speed of sound in air?sound in air?

Closed-End Air Column Closed-End Air Column ExampleExample

A closed-end air tube A closed-end air tube resonates to a tuning resonates to a tuning fork of 480 Hz at lengths fork of 480 Hz at lengths of 53.0 cm and 88.5 cm. of 53.0 cm and 88.5 cm. What is the speed of What is the speed of sound in air?sound in air?

The difference between The difference between one harmonic and the one harmonic and the next is a half-wavelength next is a half-wavelength (for open or closed-(for open or closed-ends).ends).

Closed-End Air Columns Closed-End Air Columns ExampleExample

A closed-end air tube resonates to a A closed-end air tube resonates to a tuning fork of 480 Hz at lengths of tuning fork of 480 Hz at lengths of 53.0 cm and 88.5 cm. What is the 53.0 cm and 88.5 cm. What is the speed of sound in air?speed of sound in air?

d ifference m m m

m

f H z

v f m H z ms

12 0 885 0 530 0 355

0 71

480

0 71 480 340

. . .

.

.

More PracticeMore Practice

Lab: Closed Air Lab: Closed Air Columns and the Columns and the Speed of SoundSpeed of Sound