The vibrations of a string of length `600cm` fixed at both ends are represented by the equation `y=4 sin (pi (x)/(15)) cos (96 pi t )`
where `x` and `y` are in `cm` and `t` in seconds.

Options

A. Fundamental
B. Third
C. Fourth
D. Fifth

Answer

C

Explanation

`y = 4 sin ((pi x)/15)cos (96 pit) `
This represents a stationary wave.
The harmonic mode is decided by the number of loops or
number of noodes formed on the string .
At nodes, the displacement is zero.
For this `sin ((pi x)/15) = 0 `
`:. (pi x)/15 = n pi " where " n = 0, 1, 2, 3, .....`
Thus ` x = 15`n, `:. ` for n = 0, x = 0
For n = 1 , x = 15, similarly for n = 2, 3, 4, .....
The value of x will be 30, 45, 60 cm.
x cannot be more than 60 as l = 60 cm.
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Thus there will be 5 nodes and 4 loops.
` :. ` The string will vibrate in its fourth harmonic .