# Relationship between tension and speed of a wave

### The Speed of a Wave

In this activity we will examine the precise relationship between tension (T) the force applied to the string, the wave speed (vw) and the linear mass density of the . Wave speed is equal to the square root of tension divided by the linear density Tension (F): (not frequency) in the string (t is used for time in these equations). To see how the speed of a wave on a string depends on the tension and the linear density.

The strings on a guitar have different thickness but may be made of similar material. For example, if the string has a length of 2. The guitar also has a method to change the tension of the strings.

The tension of the strings is adjusted by turning spindles, called the tuning pegs, around which the strings are wrapped. For the guitar, the linear density of the string and the tension in the string determine the speed of the waves in the string and the frequency of the sound produced is proportional to the wave speed.

## 16.3: Wave Speed on a Stretched String

Wave Speed on a String under Tension To see how the speed of a wave on a string depends on the tension and the linear density, consider a pulse sent down a taut string Figure When the taut string is at rest at the equilibrium position, the tension in the string FT is constant.

The mass element is at rest and in equilibrium and the force of tension of either side of the mass element is equal and opposite. Mass element of a string kept taut with a tension FT. The mass element is in static equilibrium, and the force of tension acting on either side of the mass element is equal in magnitude and opposite in direction.

If you pluck a string under tension, a transverse wave moves in the positive x-direction, as shown in Figure The mass element is small but is enlarged in the figure to make it visible. The sound wave travels through the medium air in this casereflects off the canyon wall and returns to its origin you.

Physics - Mechanics: Mechanical Waves (4 of 21) Finding the Tension on a String

The result is that you hear the echo the reflected sound wave of your holler. A classic physics problem goes like this: Noah stands meters away from a steep canyon wall.

He shouts and hears the echo of his voice one second later.

What is the speed of the wave? Remember, when there is a reflection, the wave doubles its distance. In other words, the distance traveled by the sound wave in 1 second is equivalent to the meters down to the canyon wall plus the meters back from the canyon wall. Variables Affecting Wave Speed What variables affect the speed at which a wave travels through a medium?

Does the frequency or wavelength of the wave affect its speed? Does the amplitude of the wave affect its speed?

## Physics Study Guide/Standing waves

Or are other variables such as the mass density of the medium or the elasticity of the medium responsible for affecting the speed of the wave? Particle 3 will be next to move because the section of string immediately to its left i. The ability of one particle to pull on its neighbors depends on how tightly the string is stretched—that is, on the tension see Section 4. The greater the tension, the greater the pulling force the particles exert on each other, and the faster the wave travels, other things being equal.

Along with the tension, a second factor influences the wave speed. For a given net pulling force, a smaller mass has a greater acceleration than a larger mass.

Therefore, other things being equal, a wave travels faster on a string whose particles have a small mass, or, as it turns out, on a string that has a small mass per unit length.

### PhysicsLAB: Relationship Between Tension in a String and Wave Speed

The mass per unit length is called the linear density of the string. The effects of the tension F and the mass per unit length are evident in the following expression for the speed v of a small-amplitude wave on a string: In these instruments, the strings are either plucked, bowed, or struck to produce transverse waves. Example 2 discusses the speed of the waves on the strings of a guitar. The effect of your adjustments on the wavelength of the wave is displayed, as is the time for the wave to travel the length of the string.

From the travel time you can assess how the speed of the wave depends on the mass of the string.