# Speed of longitudinal wave 30 times the speed of a transverse wave?

• PirateFan308
In summary: You have no way of relating L and L(0).In summary, the stress in a stretched wire of a material with a Young's modulus of Y is 30 times the stress in a wire of the same material but with a smaller modulus.
PirateFan308

## Homework Statement

What must be the stress (F/A) in a stretched wire of a material whose Young's modulus is Y for the speed of longitudinal waves to equal 30 times the speed of transverse waves?

## Homework Equations

$Y=\frac{Fl_0}{Al}$

$v_L=f\lambda = \sqrt{F/\mu}$

$v_T = \omega A sin(kx-\omega t)$

## The Attempt at a Solution

I know that $v_L=30v_T$ but my main problem is that longitudinal velocity remains constant while transverse velocity is dependent on position and time, making it impossible for one to be a multiple of the other unless they are both equal to 0, which cannot be the case. I'm not sure what I'm missing ... thanks!

PirateFan308 said:

## Homework Statement

What must be the stress (F/A) in a stretched wire of a material whose Young's modulus is Y for the speed of longitudinal waves to equal 30 times the speed of transverse waves?

those are irrevelant equations that u are using...the question says speed of transverse wave not transverse velocity of particle

PirateFan308 said:

## Homework Equations

$Y=\frac{Fl_0}{Al}$

$v_L=f\lambda = \sqrt{F/\mu}$

$v_T = \omega A sin(kx-\omega t)$

these equations are not written correct. You haven't written the formula for speed of longitudnal wave. The formula written is for the speed of transverse wave instead of longitudnal wave. The formula written for speed of Transverse wave is the formulae for "transverse velocity of particle".

darkxponent said:
these equations are not written correct. You haven't written the formula for speed of longitudnal wave. The formula written is for the speed of transverse wave instead of longitudnal wave. The formula written for speed of Transverse wave is the formulae for "transverse velocity of particle".

Is $v_T = \lambda f = \sqrt{F/\mu}$ and $v_L = \frac{Y}{\rho}$ correct?

PirateFan308 said:
Is $v_T = \lambda f = \sqrt{F/\mu}$ and $v_L = \frac{Y}{\rho}$ correct?

Hint:
You have missed a square root.

emailanmol said:
Hint:
You have missed a square root.

$v_L = \sqrt{\frac{Y}{\rho}}$??

So if $v_L=\sqrt{Y/\rho}$ and $v_t=\sqrt{F/\mu}$ then

$\sqrt{Y/\rho}=30\sqrt{F/\mu}$ which is equivalent to $Y=\frac{900F\rho}{\mu}$

$Y=\frac{Fl_0}{Al}$

so $\frac{F}{A}=\frac{Yl}{l_0}=\frac{900Fl\rho}{l_0 \mu}$

but $l\rho = A$ and $\mu = \frac{mass}{length} ~~so~~\mu l_0=mass$

so $\frac{F}{A}=\frac{mass}{900AF} ~~so~~F^2=\frac{mass}{900}$

which doesn't work ...

I also tried it a different way, letting $v_T=fλ$ so that $Y=900v^2\rho$ so then $\frac{F}{A}=\frac{Yl}{l_0} = \frac{900v^2\rho l}{l_0} = \frac{900v^2A^2}{l_0}$ which also doesn't work. Any help would be appreciated! Thanks!

Skip the step where you have got in Y=FL/AL(0).

You have no way of relating L and L(0).

Also Lp=A is not right.

p=M/V sp Lp=LM/V.
But here L is change in length.
So you can't write V=AL as L is change in length.So this doesn't help.

Y/p=900F/u.

Divide it by A on both sides

Y/Ap=900F/Au.

So F/A=Yu/900Ap

Is there any way you can find out what u/Ap is ?
( Hint:You have applied a relation between u and l in your last post.That might help)

I got it - thank you!

## What is the difference between a longitudinal wave and a transverse wave?

A longitudinal wave is a type of wave in which the disturbance or vibration is in the same direction as the propagation of the wave. In contrast, a transverse wave is a type of wave in which the disturbance or vibration is perpendicular to the direction of wave propagation.

## What is the speed of a longitudinal wave that is 30 times faster than a transverse wave?

The speed of a longitudinal wave that is 30 times faster than a transverse wave will depend on the medium through which the waves are traveling. In general, the speed of a longitudinal wave is faster than a transverse wave due to the nature of their vibrations.

## What factors affect the speed of a longitudinal wave?

The speed of a longitudinal wave can be affected by the properties of the medium, such as density, elasticity, and temperature. It can also be affected by external factors such as pressure, tension, and external forces.

## Can the speed of a longitudinal wave be faster than the speed of light?

No, according to the laws of physics, the speed of light is the fastest speed at which any object can travel. This is known as the speed of light barrier, and it applies to all types of waves, including longitudinal waves.

## What are some real-world applications of longitudinal waves?

Longitudinal waves have many practical applications, such as in medical imaging (ultrasound), communication (radio waves), and detecting earthquakes (seismic waves). They are also used in industrial settings for non-destructive testing and in the production of musical instruments such as guitars and drums.

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