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Question

A standing wave is created on a string of length 120 m and it is vibrating in 6th harmonic. Maximum possible amplitude of any particle is 10 cm and maximum possible velocity will be 10 cm/s. Which of the following statement(s) is/are correct?

A
Angular wave number (k) of the wave will be π20 cm1.
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B
Angular wave number (k) of the wave will be π10 cm1.
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C
Time period of any particles SHM will be 4π sec.
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D
Time period of any particles SHM will be 2π sec.
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Solution

The correct options are
A Angular wave number (k) of the wave will be π20 cm1.
D Time period of any particles SHM will be 2π sec.
Given that,
Length of string l=120 m
Maximum amplitude A=10 cm
Maximum speed vmax=10 cm/s
Now,
l=nλ2
6(λ2)=120 cm
λ=40 cm
k=2πλ
k=2π40
k=π20 cm1
Also
Aω=vmax
ω=vmaxA=10 cm/s10 cm
ω=1
Time period of oscillation is
T=2πω=2π sec.
Thus, options (a) and (d) are correct.

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