A longitudinal wave is represented by x =10 sin 2 π( nt -( x /λ)) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

Question

A longitudinal wave is represented by x =10 sin 2 π( nt -( x /λ)) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to: (A) 2 π (B) 5 π (C) π (D) (5 π/2)

Tardigrade Admin · Accepted Answer

V P max =4 V text wave ω A =4((ω/ k )) ⇒ A =(4 λ/2 π) λ=(2 π A /4) ⇒ (20 π/4) ⇒ 5 π

Q. A longitudinal wave is represented by $x = 10 sin 2 π (n t - \frac{x}{λ}) c m$ . The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

$2 π$

$5 π$

$π$

$\frac{5 π}{2}$

$V_{P} max = 4 V_{wave}$
$ω A = 4 (\frac{ω}{k})$
$\Rightarrow A = \frac{4 λ}{2 π}$
$λ = \frac{2 π A}{4}$
$\Rightarrow \frac{20 π}{4}$
$\Rightarrow 5 π$

Q. A longitudinal wave is represented by x=10sin2π(nt−λx​)cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

2π

5π

π

25π​

VP​max=4Vwave ​ ωA=4(kω​) ⇒A=2π4λ​ λ=42πA​ ⇒420π​ ⇒5π

Q. A longitudinal wave is represented by $x = 10 sin 2 π (n t - \frac{x}{λ}) c m$ . The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

$2 π$

$5 π$

$π$

$\frac{5 π}{2}$

$V_{P} max = 4 V_{wave}$
$ω A = 4 (\frac{ω}{k})$
$\Rightarrow A = \frac{4 λ}{2 π}$
$λ = \frac{2 π A}{4}$
$\Rightarrow \frac{20 π}{4}$
$\Rightarrow 5 π$