# Longitudinal standing waves

nil1996

## Homework Statement

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

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. NihalSh

## Homework Statement

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

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. They are similar to standing transverse waves. Think again, similar equations are used.

nil1996
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.

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

NihalSh
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.

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NihalSh
Speed of longitudinal wave in strings depends on Young's modulus.

BTW, speed of longitudinal waves in general depends on Bulk modulus.

nil1996
The term bulk modulus is used for gases and liquids. In metals we use Young's modulus, isn't it?

NihalSh
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:
nil1996
....and there goes my 100th post

thanks

NihalSh
....and there goes my 100th post

thanks

:thumbs: