A transverse wave is represented by: y = (10/π) sin ((2π/T)t-(2π/λ)x) For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

Question

A transverse wave is represented by: y = (10/π) sin ((2π/T)t-(2π/λ)x) For what value of the wavelength the wave velocity is twice the maximum particle velocity ? (A) 40 cm (B) 20 cm (C) 10 cm (D) 60 cm

Tardigrade Admin · Accepted Answer

V=2(Vp)max ∵ V=f λ f λ =2ω A λ =4π A =4π×(10/π) =40 cm

Q. A transverse wave is represented by :
$y = \frac{10}{π} sin (\frac{2 π}{T} t - \frac{2 π}{λ} x)$
For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

40 cm

20 cm

10 cm

60 cm

$V = 2 (V_{p})_{ma x}$
$∵ V = f λ$
$f λ = 2 ω A$
$λ = 4 π A$
$= 4 π \times \frac{10}{π}$
$= 40 c m$

Q. A transverse wave is represented by : y=π10​sin(T2π​t−λ2π​x) For what value of the wavelength the wave velocity is twice the maximum particle velocity ?