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Question:

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y=0.3sin(0.157x)cos(200πt). The length of the string is: (All quantities are in SI units)

80m

40m

20m

60m

Solution:

Correct option is B.
For the 4th harmonic, we have:
4λ/2 = l
2λ = l
From the equation, the wave number k = 0.157
We know that k = 2π/λ
Therefore, 2π/λ = 0.157
λ = 2π/0.157 ≈ 40 m
l = 2λ = 2 * 40 m = 80 m