# Longitudinal standing waves

1. Oct 16, 2013

### nil1996

1. The problem statement, all variables and given/known data
How to find the fundamental frequency of standing longitudinal waves?Are they similar to standing transverse waves?

2. Relevant equations
none

3. 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.

2. Oct 16, 2013

### NihalSh

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

3. Oct 16, 2013

### 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.

4. Oct 16, 2013

### nil1996

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

5. Oct 16, 2013

### NihalSh

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: Oct 16, 2013
6. Oct 16, 2013

### NihalSh

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

7. Oct 16, 2013

### nil1996

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

8. Oct 16, 2013

### NihalSh

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: Oct 16, 2013
9. Oct 16, 2013

### nil1996

....and there goes my 100th post

thanks

10. Oct 16, 2013

:thumbs: