Speed of the transverse wave in a string

When a string is attached tightly between the two points
there will be tension generated in the string. Linear density of the string can
be defined as the mass per unit length of the string. It can be proved that
velocity of the string is directly proportional to Squire root of the tension
and inversely proportional to Squire root of linear density.We can express the equation different formats as per the
requirement as shown.

If Young's modulus of the wire is given with can express the
tension in terms of Young’s modulus as shown below.

**Problem and solution**

We need the find the velocity of the wave in a stretched string using the regular formula as shown below.

**Standing waves**

Two waves of same amplitude, frequency and velocity moving in
opposite directions are superimposed then stationary waves are formed.

The superposition of the waves can be done basing on the
vector laws of addition. In the stationary waves there are some points that the
displacement is minimum and the points are called nodes. There are some other
points where the displacement is maximum and that points are called anti-nodes.
The interval between two successive who nodes as well as the anti-nodes is
always fixed as shown below.

Depending on the point of disturbance stationary waves can be
formed under different modes of vibration. At the point of disturbance the
displacement is going to be maximum and there is a formation of anti-node.
Depending on the point of disturbance, a string can vibrate under different
modes of vibration.

**Laws of stretches strings**

The frequency of a stretched string is inversely proportional
to its length when it’s tension and linear density are kept constant. This is
called law of lengths.

The frequency of stretches string is directly proportional to
Squire root of the tension when its length and linear densities are constants.
This is called law of tensions.

The frequency of a stretched string is inversely
proportional to Squire root of the linear density when the length and tension
are kept constant. This law is called as law of linear densities.

**Related Posts**

**Wave Motion an**

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