The displacement y (in cm ) produced by a simple harmonic wave is given by: y=(10/π) sin [2000 π t-(π x/17)] . The time period and maximum velocity of the particles in the medium will respectively be :

Question

The displacement y (in cm ) produced by a simple harmonic wave is given by: y=(10/π) sin [2000 π t-(π x/17)] . The time period and maximum velocity of the particles in the medium will respectively be : (A) 10-3 s , 330 ms -1 (B) 10-4 s , 20 ms -1 (C) 10-3 s , 200 ms -1 (D) 10-2 s , 2000 ms -1

Tardigrade Admin · Accepted Answer

Comparing given equation with y=A sin (ω t-k x) we get A=(10/π) cm ω=2000 π s -1 T=(2 π/ω)=10-3 s Maximum velocity =ω A=(10/π ⋅ 100) × 2000 π=200 ms -1

Q. The displacement $y$ (in $c m$ ) produced by a simple harmonic wave is given by : $y = \frac{10}{π} sin [2000 π t - \frac{π x}{17}] .$ The time period and maximum velocity of the particles in the medium will respectively be :

$1 0^{- 3} s, 330 m s^{- 1}$

$1 0^{- 4} s, 20 m s^{- 1}$

$1 0^{- 3} s, 200 m s^{- 1}$

$1 0^{- 2} s, 2000 m s^{- 1}$

Comparing given equation with $y = A sin (ω t - k x)$ we get
$A = \frac{10}{π} c m$
$ω = 2000 π s^{- 1}$
$T = \frac{2 π}{ω} = 1 0^{- 3} s$
Maximum velocity $= ω A = \frac{10}{π \cdot 100} \times 2000 π = 200 m s^{- 1}$

Q. The displacement y (in cm ) produced by a simple harmonic wave is given by : y=π10​sin[2000πt−17πx​]. The time period and maximum velocity of the particles in the medium will respectively be :

10−3s,330ms−1

10−4s,20ms−1

10−3s,200ms−1

10−2s,2000ms−1