Discussion Forum



1)

A horizontal  stretched string , fixed at two ends, is vibrating in its fifth harmonic according to the equation.   y(x,t')=(0.01m)[sin (62.8 m-1) x]  cos [(628 s-1)t].

Assuming $\pi$ =3.14 , the   correct statement (s) is (are)


A) the number of nodes is 5

B) the length of the string is 0.25m

C) the maximum displacement of the mid-point of the string from its equilibrium position is 0.01 m

D) the fundamental frequency is 100 hz

Answer:

Option B,C

Explanation:

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 Number of nodes =6

  From the given equation , we can see that 

        $k=\frac{2\pi}{\lambda}=62.8 m^{-1}$

 $\therefore$      $\lambda=\frac{2\pi}{62.8}m=0.1m$

  $l=\frac{5\lambda}{2}m=0.25m$

 The mid point  of the string is P ,an antinode

$\therefore$  maximum displacement=0.01 m 

   $\omega = 2\pi f=628 s^{-1}$

  $\therefore$     $f=\frac{628}{2\pi}=100 Hz$

 But this si fifth harmonic  freequency .

$\therefore$   Fundamental  frequency f0

   $=\frac{f}{5}=20 Hz$