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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⁻¹x)]cos[(628s⁻¹t)]. Assuming π = 3.14, the correct statement(s) is/are: The number of nodes is 5; the length of the string is 0.25m; the maximum displacement of the midpoint of the string from its equilibrium position is 0.01m; the fundamental frequency is 100Hz.

the length of the string is0.25m.

The number of nodes is5.

The maximum displacement of the midpoint of the string from its equilibrium position is0.01m.

The fundamental frequency is100Hz.

Solution:

20π = 2π/λ
λ = 1/10m = 0.1m
length of the spring = 0.5 × λ = 0.25m
Mid point is the antinode
Frequency at this mode is f = 200π/2π = 100Hz
Fundamental frequency = 100/5 = 20Hz
Therefore, correct options are B and C