SATHEE: Waves - Result Question 4

Waves - Result Question 4

4. A transverse wave is represented by $y = A \sin$ $(ω t - k x)$ . For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

[2010]

(a) $\frac{π A}{2}$

(b) $π A$

(d) $A$

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Answer:

Correct Answer: 4. (c)

Solution:

Particle velocity,

$v_{p} = \frac{d y}{d t} = A ω \cos (ω t - k x)$

$∴ v_{p max} = A ω$

wave velocity $= \frac{ω}{k}$

$∴ A ω = \frac{ω}{k}$

i.e., $A = \frac{1}{k}$ But $k = \frac{2 π}{λ}$

$∴ λ = 2 π A$

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Waves - Result Question 4

4. A transverse wave is represented by y=Asin (ωt−kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

Answer:

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4. A transverse wave is represented by $y = A \sin$ $(ω t - k x)$ . For what value of the wavelength is the wave velocity equal to the maximum particle velocity?