The displacement of a wave is represented by y = 0.6 × 10-3 sin (500 t - 0.05 x) where all the quantities are in their proper units. The maximum particle velocity (in ms-1) of the medium is

Question

The displacement of a wave is represented by y = 0.6 × 10-3 sin (500 t - 0.05 x) where all the quantities are in their proper units. The maximum particle velocity (in ms-1) of the medium is (A) 0.5 (B) 0.03 (C) 0.150 (D) 0.75

Tardigrade Admin · Accepted Answer

∵ The displacement of wave y =0.6 × 10-3 sin (500 t-0.05 x) ∴ v =(d y/d t)=0.6 × 10-3 × 500 sin (500 t-0.05 x) v =0.3 sin (500 t-0.05 x) For maximum particle velocity, sin (500 t-0.05 x)=1 Hence, V max =0.3 ms -1

Q. The displacement of a wave is represented by $y = 0.6 \times 1 0^{- 3} sin (500 t - 0.05 x)$ where all the quantities are in their proper units. The maximum particle velocity (in $m s^{- 1}$ ) of the medium is

0.5

0.03

0.150

0.75

0.3

$∵$ The displacement of wave
$y = 0.6 \times 1 0^{- 3} sin (500 t - 0.05 x)$
$∴ v = \frac{d y}{d t} = 0.6 \times 1 0^{- 3} \times 500 sin (500 t - 0.05 x)$
$v = 0.3 sin (500 t - 0.05 x)$
For maximum particle velocity,
$sin (500 t - 0.05 x) = 1$
Hence, $V_{m a x} = 0.3 m s^{- 1}$

Q. The displacement of a wave is represented by y=0.6×10−3sin(500t−0.05x) where all the quantities are in their proper units. The maximum particle velocity (in ms−1) of the medium is

0.5

0.03

0.150

0.75

0.3

∵ The displacement of wave y=0.6×10−3sin(500t−0.05x) ∴v=dtdy​=0.6×10−3×500sin(500t−0.05x) v=0.3sin(500t−0.05x) For maximum particle velocity, sin(500t−0.05x)=1 Hence, Vmax​=0.3ms−1

Q. The displacement of a wave is represented by $y = 0.6 \times 1 0^{- 3} sin (500 t - 0.05 x)$ where all the quantities are in their proper units. The maximum particle velocity (in $m s^{- 1}$ ) of the medium is

$∵$ The displacement of wave
$y = 0.6 \times 1 0^{- 3} sin (500 t - 0.05 x)$
$∴ v = \frac{d y}{d t} = 0.6 \times 1 0^{- 3} \times 500 sin (500 t - 0.05 x)$
$v = 0.3 sin (500 t - 0.05 x)$
For maximum particle velocity,
$sin (500 t - 0.05 x) = 1$
Hence, $V_{m a x} = 0.3 m s^{- 1}$