The linear density of a vibrating string is 1.3× 10- 4 kg m- 1 . A transverse wave is propagating on the string and its described by the equation y=0.021sin (x + 30 t) , where x and y are measured in m and t in s . The tension in the string is

Question

The linear density of a vibrating string is 1.3× 10- 4 kg m- 1 . A transverse wave is propagating on the string and its described by the equation y=0.021sin (x + 30 t) , where x and y are measured in m and t in s . The tension in the string is (A) 0.12 N (B) 0.48 N (C) 1.20 N (D) 4.80 N

Tardigrade Admin · Accepted Answer

m=1.3× 10- 4 kg m- 1 From Eq., k=1 m- 1 , ω =30 s- 1 Wave velocity v=(ω /k)=30m / s Wave speed on vibrating string, v=√(T/m) 30=√(T/1.3 × 1 0- 4) T=(1.3 × 1 0- 4)900 T=0.12 N

Q. The linear density of a vibrating string is $1.3 \times 1 0^{- 4} k g m^{- 1}$ . A transverse wave is propagating on the string and its described by the equation $y = 0.021 s in (x + 30 t)$ , where $x$ and $y$ are measured in $m$ and $t$ in $s$ . The tension in the string is

$0.12 N$

$0.48 N$

$1.20 N$

$4.80 N$

$m = 1.3 \times 1 0^{- 4} k g m^{- 1}$
From Eq., $k = 1 m^{- 1}$ , $ω = 30 s^{- 1}$
Wave velocity $v = \frac{ω}{k} = 30 m / s$
Wave speed on vibrating string,
$v = \frac{T}{m}$
$30 = \frac{T}{1.3 \times 1 0 ^{- 4}}$
$T = (1.3 \times 1 0^{- 4}) 900$
$T = 0.12 N$

Q. The linear density of a vibrating string is 1.3×10−4kgm−1 . A transverse wave is propagating on the string and its described by the equation y=0.021sin(x+30t) , where x and y are measured in m and t in s . The tension in the string is

0.12N

0.48N

1.20N

4.80N