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The vibrations of a string of length 60 ...

The vibrations of a string of length 60 cm fixed at both ends are represented by the equation `y=4sin((pix)/15) cos (96 pi t)`, where x and y are in cm and t in seconds.
(a)What is the maximum displacement of a point at `x = 5cm`?
(b)Where are the nodes located along the string?
(c)What is the velocity of the particle at x=7.5cm and t=0.25s?
(d)Write down the equations of the component waves whose superposition gives the above wave.

A

The maximum displacement of a point `x = 5 cm` is `2sqrt(3) cm`.

B

The nodes located along the string are at a distance of `15n` where integer `n` varies from `0` to `40`.

C

The velocity of the particle at `x = 7.5 cm` at `t = 0.25` sec is `0`

D

The equations of the component waves whose superposition gives the above wave are
`2 sin 2pi ((x)/(30) + 48t), 2 sin 2pi((x)/(30) - 48t)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
compare with `y = A sin Kx cos omegat`
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