Longitudinal standing waves

In summary, the homework statement asks for the ratio of the fundamental frequency of longitudinal waves in a string to that of transverse waves. The equations used are similar, but the problem statement asks for the ratio of two different frequencies. When calculating the speed of longitudinal waves in a string, Young's modulus is used.
  • #1
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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:
 
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  • #2
nil1996 said:

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
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
Ok i got this question right. Speed of longitudinal wave in strings depends on Young's modulus.
 
  • #5
nil1996 said:
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
nil1996 said:
Speed of longitudinal wave in strings depends on Young's modulus.

BTW, speed of longitudinal waves in general depends on Bulk modulus.
 
  • #7
The term bulk modulus is used for gases and liquids. In metals we use Young's modulus, isn't it?
 
  • #8
nil1996 said:
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.
 
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  • #9
...and there goes my 100th post

thanks
 
  • #10
nil1996 said:
...and there goes my 100th post

thanks

:thumbs:
 

1. What are longitudinal standing waves?

Longitudinal standing waves are a type of standing wave that occurs when a wave oscillates in the same direction as its propagation. This means that the particles of the medium are moving back and forth parallel to the direction of the wave's movement.

2. How are longitudinal standing waves different from transverse standing waves?

Longitudinal standing waves are different from transverse standing waves in terms of the direction of particle oscillation. In transverse standing waves, the particles of the medium move perpendicular to the direction of the wave's movement. In longitudinal standing waves, the particles move parallel to the direction of the wave.

3. What causes longitudinal standing waves to form?

Longitudinal standing waves are formed when two waves of the same frequency and amplitude travel in opposite directions through a medium. The interference between these waves creates points of constructive and destructive interference, resulting in a stationary pattern.

4. How are nodes and antinodes related to longitudinal standing waves?

Nodes and antinodes are points along a longitudinal standing wave where the amplitude of the wave is either zero (nodes) or maximum (antinodes). These points are created due to the interference between the two traveling waves and can be seen as the points where the particles of the medium do not move or move with the greatest amplitude, respectively.

5. What are some real-life examples of longitudinal standing waves?

Longitudinal standing waves can be observed in various real-life scenarios, such as in musical instruments, where the air column inside the instrument vibrates in a longitudinal standing wave pattern to produce different notes. They can also be seen in earthquakes, where seismic waves travel through the earth's crust in a longitudinal standing wave pattern. Additionally, they are used in medical imaging techniques like ultrasound, where sound waves are used to create images of internal structures in the body.

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