Question

The vibrations of a string of length 60cm fixed at both ends are represented by the equation---------------------------- y = 4 sin ((pix)/(15)) cos (96 pit) Where x and y are in cm and t in seconds. (i) What is the maximum displacement of a point at x = 5cm? (ii) Where are the nodes located along the string? (iii) What is the velocity of the particle at x = 7.5 cm at t = 0.25 sec.? (iv) Write down the equations of the component waves whose superpositions gives the above wave

Answer 1

Answer:

the equation will be

A+sin(wt+theta)

Answer 2

Given

Y = 2 sin(4πx/15) cos(96πt) ........(1)

This equation represents the stationalry equation of the type

Y = 2a sin(2πx/λ) cos(96πt)........(2)

Compairing the equations we get,

2πx/λ = 4πx/15

$$\lambda = 7.5 cm$$

The string is of length 60 cm while the wavelenght is 7.5 cm, hence location of nodes are

$$x = 0, 7.5/2, 7.5, 11.25, 15, . . . . . , 60.$$

hence maximum number of loops formed is 16.