The displacement y of a particle in a medium can be expressed as: y=10-6 sin (100 t+20 x+π / 4) m , where t is in second and x in meter. The speed of the wave is

Question

The displacement y of a particle in a medium can be expressed as: y=10-6 sin (100 t+20 x+π / 4) m , where t is in second and x in meter. The speed of the wave is (A) 2000 m / s (B) 5 m / s (C) 20 m / s (D) 5 π m / s.

Tardigrade Admin · Accepted Answer

Given wave equation: y=10-6 sin (100 t+20 x+(π/4)) m Standard equation: y=a sin (ω t+k x+φ) Compare the two ∴ ω=100 and k=20 ∴ (ω/k)=(100/20) ⇒ (2 π n/2 π / λ)=n λ=v=5 ∴ v=5 m / s

Q. The displacement $y$ of a particle in a medium can be expressed as:

$y = 1 0^{- 6} sin (100 t + 20 x + π /4) m,$ where $t$ is in second and

$x$ in meter. The speed of the wave is

2000 m / s

5 m / s

20 m / s

$5 πm / s$ .

Given wave equation :
$y = 1 0^{- 6} sin (100 t + 20 x + \frac{π}{4}) m$
Standard equation $: y = a sin (ω t + k x + ϕ)$
Compare the two
$∴ ω = 100$ and $k = 20$
$∴ \frac{ω}{k} = \frac{100}{20}$
$\Rightarrow \frac{2 πn}{2 π / λ} = nλ = v = 5$
$∴ v = 5 m / s$

Q. The displacement y of a particle in a medium can be expressed as: y=10−6sin(100t+20x+π/4)m, where t is in second and x in meter. The speed of the wave is