First slide

Speed of wave

Question

A transverse wave is represented by $y = A \sin (ωt - kx)$ . For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

Moderate

A

$\frac{πA}{2}$
B

$πA$
C

2 $πA$
D

A

Solution

Wave velocity v = $\frac{λ}{T} = \frac{ωλ}{2 π}$
Maximum particle velocity ${(v_{\max})}_{ρ}$ = $Aω$
Given, $v = {(v_{\max})}_{ρ}$
$\frac{ωλ}{2 π} = Aω \Rightarrow λ = 2 πA$

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