Question

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)x] cos[(628s^-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) The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01m.

(D) The fundamental frequency is 100 Hz.

Answer 1

(B) the length of the string is 0.25 m. 

(C) The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01m.

length of the spring = 0.5 x 1/2 = 0.25

Mid point is the antinode 

Frequency at this mode is f = 200π / 2π = 100Hz

∴ Fundamental frequency = 100/5 = 20Hz