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

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 = 0.3 sin(0.157 x) cos(200π t). The length of the string is: (All quantities are in SI units.) (A) 20 m (B) 80 m (C) 60 m (D) 40 m

Tardigrade Admin · Accepted Answer

4th harmonic 4 (λ/2) = ℓ 2 λ = ℓ From equation (2 π/λ) = 0.157 λ = 40 ℓ = 2λ = 80 m Option (2)

Q. A string is clamped at both the ends and it is vibrating in its $4^{t h}$ harmonic. The equation of the stationary wave is $Y = 0.3 s in (0.157 x) cos (200 π t$ ). The length of the string is : (All quantities are in SI units.)

20 m

80 m

60 m

40 m

4^th harmonic
$4 \frac{λ}{2} = ℓ$
$2 λ = ℓ$
From equation $\frac{2 π}{λ} = 0.157$
$λ = 40$
$ℓ = 2 λ$
$= 80 m$
Option (2)

Q. 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.)