A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t)=(0.01 m ) sin [(62.8 m -1) ×] cos [(628 s -1) t] . Assuming π=3.14, the correct statement(s) is (are):

Question

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t)=(0.01 m ) sin [(62.8 m -1) ×] 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 0.25 m. (C) 3.3 × 10-11 Wb The maximum displacement of the midpoint of the string its equilibrium position is 0.01 m. (D) The fundamental frequency is 100 Hz.

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e560f29c410db8d77eab1c01accf69bb-.png" /> (A) There are 5 complete loops. Total number of nodes =6 (B) ω=628 sec -1 k =62.8 m -1=(2 π/λ) ⇒ λ=(1/10) Vw=(ω/k)=(628/62.8)=10 ms -1 L =(5 λ/2)=0.25 (c) 2 A =0.01= maximum amplitude of antinode

Q. A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, $y (x, t) = (0.01 m) sin [(62.8 m^{- 1}) \times] cos [(628 s^{- 1}) t]$ . Assuming $π = 3.14$ , the correct statement(s) is (are):

The number of nodes is $5$ ,

The length of the string is $0.25 m$ .

3.3 $\times 1 0^{- 11} Wb$ The maximum displacement of the midpoint of the string its equilibrium position is $0.01 m$ .

The fundamental frequency is $100 Hz$ .

(A) There are $5$ complete loops. Total number of nodes $= 6$
(B) $ω = 628 se c^{- 1}$
$k = 62.8 m^{- 1} = \frac{2 π}{λ} \Rightarrow λ = \frac{1}{10}$
$V_{w} = \frac{ω}{k} = \frac{628}{62.8} = 10 m s^{- 1}$
$L = \frac{5 λ}{2} = 0.25$
(c) $2 A = 0.01 =$ maximum amplitude of antinode

Q. A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x,t)=(0.01m)sin[(62.8m−1)×]cos[(628s−1)t] . Assuming π=3.14, the correct statement(s) is (are):

The number of nodes is 5 ,

The length of the string is 0.25m.

3.3 ×10−11Wb The maximum displacement of the midpoint of the string its equilibrium position is 0.01m.

The fundamental frequency is 100Hz.