Two points on string are being observed as a travelling wave passes them- The points are at x 1-0 and x 2-1 m- the transverse motions of two points are found to be as follows y 1- A sin 3 - t and y 2- A sin3 - t -8 - t is in seconds and y in metre- Mark correct optionsA- Frequency of wave is 3 HZB- Frequency of wave is 1-5 HzC- Wavelength may be 16 mD- Wavelength may be 16-15 m

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Standard XII

Physics

Speed in a Medium

Two points on...

Question

Two points on string are being observed as a travelling wave passes them. The points are at $x_{1} = 0 a n d x_{2} = l m$ , the transverse motions of two points are found to be as follows $y_{1} = A s i n (3 π t) a n d y_{2} = A s i n (3 π t + \frac{π}{8})$ ; t is in seconds and y in metre. Mark correct options

Frequency of wave is 3 HZ

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Frequency of wave is 1.5 Hz

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Wavelength may be 16 m

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Wavelength may be

\frac{16}{15} m

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Solution

The correct options are
B Frequency of wave is 1.5 Hz
C Wavelength may be 16 m
$y_{1} = A s i n 3 π t y_{2} = A s i n (3 π t + \frac{π}{8}) ∴ ϕ = \frac{π}{8} a n d 2 π v = 3 π ∴ v = 1.5 A s k = \frac{ω}{v} a n d ϕ = k x ∴ \frac{3 π}{v} \times 1 = \frac{π}{8} \Rightarrow v = 24 \frac{m}{s} ∴ λ = \frac{24 \times 2}{3} = 16 m$

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Two points on string are being observed as a travelling wave passes them. The points are at x1=0 and x2=l m, the transverse motions of two points are found to be as follows y1=A sin (3 πt) and y2=A sin(3πt+π8) ; t is in seconds and y in metre. Mark correct options

The correct options are B Frequency of wave is 1.5 Hz C Wavelength may be 16 m y1=A sin 3πty2=A sin (3πt+π8)∴ ϕ=π8 and 2πv=3π ∴ v=1.5Ask =ωv and ϕ=kx ∴ 3πv×1=π8⇒ v=24ms ∴ λ=24×23=16 m