<< Chapter < Page Chapter >> Page >

A guitar string of length L is bound at both ends. [link] shows the string’s harmonic frequencies when struck.

Harmonic Number Frequency
1 225/ L
2 450/ L
3 675/ L
4 900/ L
  1. Based on the information above, what is the speed of the wave within the string?
  2. The guitarist then slides her finger along the neck of the guitar, changing the string length as a result. Calculate the fundamental frequency of the string and wave speed present if the string length is reduced to 2/3 L .
Got questions? Get instant answers now!

Section summary

  • Sound interference and resonance have the same properties as defined for all waves.
  • In air columns, the lowest-frequency resonance is called the fundamental, whereas all higher resonant frequencies are called overtones. Collectively, they are called harmonics.
  • The resonant frequencies of a tube closed at one end are:
    f n = n v w 4 L n = 1, 3, 5 . . ., size 12{n=1,3,5 "." "." "." } {}
    f 1 size 12{f rSub { size 8{1} } } {} is the fundamental and L size 12{L} {} is the length of the tube.
  • The resonant frequencies of a tube open at both ends are:
    f n = n v w 2 L n = 1, 2, 3 . . . size 12{n=1,3,5 "." "." "." } {}

Conceptual questions

How does an unamplified guitar produce sounds so much more intense than those of a plucked string held taut by a simple stick?

Got questions? Get instant answers now!

You are given two wind instruments of identical length. One is open at both ends, whereas the other is closed at one end. Which is able to produce the lowest frequency?

Got questions? Get instant answers now!

What is the difference between an overtone and a harmonic? Are all harmonics overtones? Are all overtones harmonics?

Got questions? Get instant answers now!

Problems&Exercises

A “showy” custom-built car has two brass horns that are supposed to produce the same frequency but actually emit 263.8 and 264.5 Hz. What beat frequency is produced?

0.7 Hz

Got questions? Get instant answers now!

What beat frequencies will be present: (a) If the musical notes A and C are played together (frequencies of 220 and 264 Hz)? (b) If D and F are played together (frequencies of 297 and 352 Hz)? (c) If all four are played together?

Got questions? Get instant answers now!

What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?

0.3 Hz, 0.2 Hz, 0.5 Hz

Got questions? Get instant answers now!

A piano tuner hears a beat every 2.00 s when listening to a 264.0-Hz tuning fork and a single piano string. What are the two possible frequencies of the string?

Got questions? Get instant answers now!

(a) What is the fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?

(a) 256 Hz

(b) 512 Hz

Got questions? Get instant answers now!

If a wind instrument, such as a tuba, has a fundamental frequency of 32.0 Hz, what are its first three overtones? It is closed at one end. (The overtones of a real tuba are more complex than this example, because it is a tapered tube.)

Got questions? Get instant answers now!

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end.)

180 Hz, 270 Hz, 360 Hz

Got questions? Get instant answers now!

How long must a flute be in order to have a fundamental frequency of 262 Hz (this frequency corresponds to middle C on the evenly tempered chromatic scale) on a day when air temperature is 20.0ºC ? It is open at both ends.

Got questions? Get instant answers now!

What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

1.56 m

Got questions? Get instant answers now!

What is the length of a tube that has a fundamental frequency of 176 Hz and a first overtone of 352 Hz if the speed of sound is 343 m/s?

Got questions? Get instant answers now!

(a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is 18.0ºC . (b) What is its fundamental frequency at 25.0ºC ?

(a) 0.334 m

(b) 259 Hz

Got questions? Get instant answers now!

By what fraction will the frequencies produced by a wind instrument change when air temperature goes from 10.0ºC to 30.0ºC ? That is, find the ratio of the frequencies at those temperatures.

Got questions? Get instant answers now!

The ear canal resonates like a tube closed at one end. (See [link] .) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be 37.0ºC , which is the same as body temperature. How does this result correlate with the intensity versus frequency graph ( [link] of the human ear?

3.39 to 4.90 kHz

Got questions? Get instant answers now!

Calculate the first overtone in an ear canal, which resonates like a 2.40-cm-long tube closed at one end, by taking air temperature to be 37.0ºC . Is the ear particularly sensitive to such a frequency? (The resonances of the ear canal are complicated by its nonuniform shape, which we shall ignore.)

Got questions? Get instant answers now!

A crude approximation of voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end. (See [link] .) (a) What is the fundamental frequency if the tube is 0.240-m long, by taking air temperature to be 37.0ºC ? (b) What would this frequency become if the person replaced the air with helium? Assume the same temperature dependence for helium as for air.

(a) 367 Hz

(b) 1.07 kHz

Got questions? Get instant answers now!

(a) Students in a physics lab are asked to find the length of an air column in a tube closed at one end that has a fundamental frequency of 256 Hz. They hold the tube vertically and fill it with water to the top, then lower the water while a 256-Hz tuning fork is rung and listen for the first resonance. What is the air temperature if the resonance occurs for a length of 0.336 m? (b) At what length will they observe the second resonance (first overtone)?

Got questions? Get instant answers now!

What frequencies will a 1.80-m-long tube produce in the audible range at 20.0ºC if: (a) The tube is closed at one end? (b) It is open at both ends?

(a) f n = n ( 47.6 Hz ) , n = 1, 3, 5,..., 419

(b) f n = n ( 95.3 Hz ) , n = 1, 2, 3,..., 210

Got questions? Get instant answers now!

Questions & Answers

what is power?
aron Reply
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
Alona Reply
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
Kavita Reply
hi
Godfred
what about the wind vane
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
Anurag Reply
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
Jaydie Reply
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
Princewill Reply
how can I read physics...am finding it difficult to understand...pls help
rerry Reply
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju
I have a exam on 12 february
David Reply
what is velocity
Jiti
the speed of something in a given direction.
Ju
what is a magnitude in physics
Jiti Reply
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
Practice Key Terms 5

Get the best College physics for ap... course in your pocket!





Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask