## Tuesday, January 6, 2015

### Frequency of Stationary wave in a streched String

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.

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Wave Motion an introduction