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Q.

A string of uniform cross-sectional area is hanging from one of tis ends as shown in figure. A transverse sinusoidal pulse is generated at the lower end and the pulse is propagating up the string. If the wavelength of wave at the mid-point C is λ, what is the wavelength at the uppermost point A?

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a

λ2

b

2λ

c

λ2

d

2 λ

answer is D.

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Detailed Solution

Velocity of wave at a distance x from the lower end is Vx=gx.Frequency (f) of wave remains unchanged throughout the length of the string. Therefore wave length λx at a distance x from the lower end is given by λx=Vxf=gxf⇒λx∝x∴ λAλC=xAxC⇒λAλ=ll/2⇒λA=2 λ

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A string of uniform cross-sectional area is hanging from one of tis ends as shown in figure. A transverse sinusoidal pulse is generated at the lower end and the pulse is propagating up the string. If the wavelength of wave at the mid-point C is λ, what is the wavelength at the uppermost point A?