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Longitudinal standing waves

  • Thread starter nil1996
  • Start date
  • #1
301
7

Homework Statement


How to find the fundamental frequency of standing longitudinal waves?Are they similar to standing transverse waves?

Homework Equations


none


The Attempt at a Solution


I know pretty much about standing transverse waves in strings. But i am confused about standing longitudinal waves in strings.:confused:
 

Answers and Replies

  • #2
199
15

Homework Statement


How to find the fundamental frequency of standing longitudinal waves?Are they similar to standing transverse waves?

Homework Equations


none


The Attempt at a Solution


I know pretty much about standing transverse waves in strings. But i am confused about standing longitudinal waves in strings.:confused:
They are similar to standing transverse waves. Think again, similar equations are used.
 
  • #3
301
7
The problem statement is-
A string is stretched so that its length is increased by 1/n of its original length. Find the ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration.
 
  • #4
301
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Ok i got this question right. Speed of longitudinal wave in strings depends on Young's modulus.
 
  • #5
199
15
The problem statement is-
A string is stretched so that its length is increased by 1/n of its original length. Find the ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration.
A string forms transverse wave, not longitudinal wave. maybe the question wants you to assume longitudinal wave traveling through a tube (and its length is increased) and calculate the ratio between the two.

Edit: great, that you got it!!!.....I guess I overlooked the question, the question was asking about the longitudinal waves that travel through every material medium or maybe longitudinal term was misprinted.
 
Last edited:
  • #6
199
15
Speed of longitudinal wave in strings depends on Young's modulus.
BTW, speed of longitudinal waves in general depends on Bulk modulus.
 
  • #7
301
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The term bulk modulus is used for gases and liquids. In metals we use Young's modulus, isn't it?
 
  • #8
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The term bulk modulus is used for gases and liquids. In metals we use Young's modulus, isn't it?
Bulk modulus is also used for solids/metal. For tensile stress young's modulus is used, for hydraulic stress bulk modulus is used.

$$v_{transverse}=\sqrt{\frac{T}{μ}}$$
$$v_{longitudinal}=\sqrt{\frac{B}{ρ}}$$
##T## is Tension.
##μ## is linear mass density
##B## is Bulk modulus
##ρ## is density

Edit: Tension can be related to young's modulus by:
$$T=Y.A.\frac{ΔL}{L}$$
##Y## is young's modulus
##A## is cross-sectional area.
##L## is initial length of the string.
 
Last edited:
  • #9
301
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....and there goes my 100th post

thanks
 
  • #10
199
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....and there goes my 100th post

thanks
:thumbs:
 

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