The equation of a wave is $y = 4 sin \frac{π}{2} (2 t + \frac{x}{8})$ where, $y, x$ are in $c m$ and time in $s e c o n d s$ . The amplitude, wavelength, velocity and frequency of the wave are, respectively :

4 c m, 32 c m, 16 c m / s, 0.5 H z

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8 c m, 16 c m, 32 c m / s, 1.0 H z

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4 c m, 32 c m, 32 c m / s, 0.5 H z

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8 c m, 16 c m, 16 c m / s, 1.0 H z

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Solution

The correct option is A $4 c m, 32 c m, 16 c m / s, 0.5 H z$
$y = A sin (ω t + k x)$
$y = 4 sin (π f + \frac{π x}{16})$
$A = 4 c m$ ; $ω = π$ ; $k = \frac{π}{16}$ ; $λ = \frac{2 π}{k}$ $λ = \frac{2 π \times 16}{π}$ $= 32 c m$
$\frac{ω}{V} = \frac{2 π}{λ} = k$

$\frac{π}{V} = \frac{π}{16}$ ; $V = 16 c m / s e c$ ; $T = \frac{2 π}{ω}$

$T = \frac{2 π}{π}$ $= 2$
$f = \frac{1}{T}$ $= 0.5 H z$

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The equation of a wave is y=4sinπ2(2t+x8) where, y,x are in cm and time in seconds. The amplitude, wavelength, velocity and frequency of the wave are, respectively :

The correct option is A 4 cm,32 cm,16 cm/s,0.5Hzy=Asin(ωt+kx)y=4sin(πf+πx16)A=4cm ; ω=π ; k=π16 ; λ=2πk λ=2π×16π =32cmωV=2πλ=kπV=π16 ; V=16cm/sec ; T=2πω T=2ππ =2f=1T = 0.5Hz

The equation of a wave is $y = 4 sin \frac{π}{2} (2 t + \frac{x}{8})$ where, $y, x$ are in $c m$ and time in $s e c o n d s$ . The amplitude, wavelength, velocity and frequency of the wave are, respectively :