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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 π =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:

842021558_m4.JPG

 Number of nodes =6

  From the given equation , we can see that 

        k=2πλ=62.8m1

       λ=2π62.8m=0.1m

  l=5λ2m=0.25m

 The mid point  of the string is P ,an antinode

  maximum displacement=0.01 m 

   ω=2πf=628s1

       f=6282π=100Hz

 But this si fifth harmonic  freequency .

   Fundamental  frequency f0

   =f5=20Hz