A standing wave is created on a string of length 120m 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 π20cm−1.
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B
Angular wave number (k) of the wave will be π10cm−1.
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C
Time period of any particles SHM will be 4πsec.
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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 π20cm−1. 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=π20cm−1 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.