The equation of a simple harmonic wave is given by
$y = 3 sin \frac{π}{2} (50 t - x)$
where $x$ and $y$ are in meters and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:

Question

The equation of a simple harmonic wave is given by

y = 3 sin \frac{π}{2} (50 t - x)

where

x

and

y

are in meters and

t

is in seconds. The ratio of maximum particle velocity to the wave velocity is:

Toppr Admin · Accepted Answer

The correct option is A 32-x3C0-From the wave equations- we know thatvmax-a-x3C9-v-n-x3BB-vmaxv-a-x3C9-n-x3BB-a-2-x3C0-n-n-x3BB-2-x3C0-a-x3BB-2-x3C0-a2-x3C0-K-Ka-x3C0-2-xD7-3-3-x3C0-2

The equation of a simple harmonic wave is given by
$y = 3 sin \frac{π}{2} (50 t - x)$
where $x$ and $y$ are in meters and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:
$\frac{2}{3} π$
$3 π$
$2 π$
$\frac{3}{2} π$

The correct option is A $\frac{3}{2} π$
From the wave equations, we know that
$v_{m a x} = a ω$
$v = n λ$
$\frac{v_{m a x}}{v} = \frac{a ω}{n λ} = \frac{a (2 π n)}{n λ} = \frac{2 π a}{λ} = \frac{2 π a}{\frac{2 π}{K}}$
$= K a = \frac{π}{2} \times 3 = \frac{3 π}{2}$

The equation of a simple harmonic wave is given byy=3sinπ2(50t−x)where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is:23π3π2π32π

The correct option is A 32πFrom the wave equations, we know thatvmax=aωv=nλvmaxv=aωnλ=a(2πn)nλ=2πaλ=2πa2πK=Ka=π2×3=3π2

The equation of a simple harmonic wave is given by
$y = 3 sin \frac{π}{2} (50 t - x)$
where $x$ and $y$ are in meters and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:
$\frac{2}{3} π$
$3 π$
$2 π$
$\frac{3}{2} π$

The correct option is A $\frac{3}{2} π$
From the wave equations, we know that
$v_{m a x} = a ω$
$v = n λ$
$\frac{v_{m a x}}{v} = \frac{a ω}{n λ} = \frac{a (2 π n)}{n λ} = \frac{2 π a}{λ} = \frac{2 π a}{\frac{2 π}{K}}$
$= K a = \frac{π}{2} \times 3 = \frac{3 π}{2}$