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Q.

A block of mass M is suspended by a thin string of mass M  and length l. A transverse wave of wavelength λ0 is produced at the lower end A of the string. The wave propagates up the string. What will be the wave length when the wave arrives at the upper end O of the string?

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a

2λ0

b

λ0/2

c

2λ0

d

λ0/22

answer is A.

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Detailed Solution

If μ be the mass per unit length of the string, then T0=Tension at upper end=(μl+M)g=2μlgTA=Tension at lower end=mg=μl g∴ V0=T0μ=2gl and  VA=TAμ=glFrequency of wave remains constant ∴ νλ=VO and νλ0=VA∴ λλ0=V0VA=2glgl⇒λ=2λ0
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