# How Does Doubling the Mass Affect Wave Speed on a Wire?

• valeriex0x
In summary, the speed of waves on a vertical wire with a hanging mass depends on the tension and mass per unit length. The equation for this is v = √(T/μ), where T is the tension and μ is the mass per unit length. The question asks for the speed in terms of V if the mass is doubled without changing the tension or length of the wire. The answer is not √2, but can be found using the given equation.
valeriex0x

## Homework Statement

When a mass M hangs from a vertical wire of length L, waves travel on this wire with a speed V.

a) What will be the speed of these waves in terms of V if we double M without stretching the wire?

V=?

Good morning, could someone please tell me why my answer of rad 2 is wrong. I thought i was on the right track.

## Homework Equations

See uploaded photo of all work

## The Attempt at a Solution

see uploaded photo of all work

#### Attachments

• IMG_0656.jpg
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The speed of a wave along a stretched string depends on the tension in the string and the mass per unit length.

v = √(T/μ) where T = tension in the string and μ = mass per unit length.
Can you get it from this??
What do you mean by rad2...

Do you mean root2 (√2) ?

## What is the speed of a mechanical wave?

The speed of a mechanical wave is the rate at which the wave travels through a medium. It is measured in meters per second (m/s).

## How is the speed of a mechanical wave calculated?

The speed of a mechanical wave is calculated by dividing the wavelength of the wave by its period. This can also be expressed as the product of the wave's frequency and wavelength.

## Does the speed of a mechanical wave depend on the medium it travels through?

Yes, the speed of a mechanical wave is affected by the properties of the medium it travels through, such as density, elasticity, and temperature.

## What is the fastest speed at which a mechanical wave can travel?

The fastest speed at which a mechanical wave can travel is the speed of sound in a medium. This speed varies depending on the properties of the medium, but in air at room temperature, it is approximately 343 m/s.

## Can the speed of a mechanical wave be changed?

Yes, the speed of a mechanical wave can be changed by altering the properties of the medium it travels through. For example, the speed of sound can be increased by increasing the temperature of the medium.

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