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Question

A standing wave is created on a string fixed at both ends, of length 120 cm 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 option is D Time period of any particles SHM will be 2π sec.
Given that,
Length of string l=120 cm
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 rad/s
Time period of oscillation is
T=2πω=2π sec.
Thus, options (a) and (d) are correct.

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