A transverse wave described by equation y=0.02 sin (x+30 t ) (where x and t are in metres and seconds, respectively) is travelling along a wire of area of cross-section 1 mm 2 and density 8000 kg / m 3. What is the tension in the string?

Question

A transverse wave described by equation y=0.02 sin (x+30 t ) (where x and t are in metres and seconds, respectively) is travelling along a wire of area of cross-section 1 mm 2 and density 8000 kg / m 3. What is the tension in the string? (A) 20 N (B) 7.2 N (C) 30 N (D) 14.4 N

Tardigrade Admin · Accepted Answer

y=0.02 sin (x+30 t) For the given wave: v=(d x/d t)=-30 (x+30 t= constant) We have v=√(T/μ) ⇒ T=μ v2=A ⋅ ρ V2 =(10-6 m 2)(8 × 103 ( kg / m 3))(30)2 ⇒ T= 7.2 N

Q. A transverse wave described by equation $y = 0.02 sin (x + 30 t$ ) (where $x$ and $t$ are in metres and seconds, respectively) is travelling along a wire of area of cross-section $1 m m^{2}$ and density $8000 k g / m^{3}$ . What is the tension in the string?

20 N

7.2 N

30 N

14.4 N

$y = 0.02 sin (x + 30 t)$
For the given wave: $v = \frac{d x}{d t} = - 30$
( $x + 30 t =$ constant)
We have
$v = \frac{T}{μ} \Rightarrow T = μ v^{2} = A \cdot ρ V^{2}$
$= (1 0^{- 6} m^{2}) (8 \times 1 0^{3} \frac{k g}{m ^{3}}) (30)^{2}$
$\Rightarrow T = 7.2 N$

Q. A transverse wave described by equation y=0.02sin(x+30t ) (where x and t are in metres and seconds, respectively) is travelling along a wire of area of cross-section 1mm2 and density 8000kg/m3. What is the tension in the string?