A transverse wave is represented by y=2 sin (ω t-k x). The wavelength for which wave-velocity is equal to the maximum particle velocity, is m

Question

A transverse wave is represented by y=2 sin (ω t-k x). The wavelength for which wave-velocity is equal to the maximum particle velocity, is m (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Wave velocity, v=(ω/k) Particle velocity, vp=(d y/d t)=A ω cos (ω t-k x) ∴ ( v p ) max = A ω A ω=(ω/ k ) ⋅s (given) ⇒ A =(λ/2 π) ⇒ λ=2 π A =4 π=12.56 m

Q. A transverse wave is represented by $y = 2 sin (ω t - k x)$ . The wavelength for which wave-velocity is equal to the maximum particle velocity, is_____ $m$

Wave velocity, $v = \frac{ω}{k}$
Particle velocity, $v_{p} = \frac{d y}{d t} = A ω cos (ω t - k x)$
$∴ (v_{p})_{m a x} = A ω$
$A ω = \frac{ω}{k} \dots$ (given)
$\Rightarrow A = \frac{λ}{2 π}$
$\Rightarrow λ = 2 π A = 4 π = 12.56 m$

Q. A transverse wave is represented by y=2sin(ωt−kx). The wavelength for which wave-velocity is equal to the maximum particle velocity, is_____ m

Wave velocity, v=kω​ Particle velocity, vp​=dtdy​=Aωcos(ωt−kx) ∴(vp​)max​=Aω Aω=kω​⋯ (given) ⇒A=2πλ​ ⇒λ=2πA=4π=12.56m

Q. A transverse wave is represented by $y = 2 sin (ω t - k x)$ . The wavelength for which wave-velocity is equal to the maximum particle velocity, is_____ $m$

Wave velocity, $v = \frac{ω}{k}$
Particle velocity, $v_{p} = \frac{d y}{d t} = A ω cos (ω t - k x)$
$∴ (v_{p})_{m a x} = A ω$
$A ω = \frac{ω}{k} \dots$ (given)
$\Rightarrow A = \frac{λ}{2 π}$
$\Rightarrow λ = 2 π A = 4 π = 12.56 m$