A. A displacement node occurs at x = 0.15 m
B. An antinode occurs at `x = 0.3 m`
C. The wavelength of the wave is 0.2 m
D. The speed of the wave is 5.0 m/s
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Correct Answer – A::B::C::D
`(2pi)/(lamda)=10pi rArrlamda=0.2m`
Node occurs at `x=(lamda)/(4),(3lamda)/(4), (5lamda)/(4)=0.05m`
`0.15 m`
Antinode occurs at `x=(lamda)/(2),lamda,3(lamda)/(2)`….=
`0.1 m,0.2,0.3m`
`v = (50 pi)/(10 pi) = 5 m//s`
Correct Answer – A::B::C::D
Correct Answer – C
( c ) Comaring it with
`y(x, t) = A cos(omegat + pi//2)coos k x`
If `k x = pi//2`, a node occurs,
:. `10pi x = pi//2 rArr x = 0.05m`
If `k x = pi`,an antinode occurs
rArr `10pix = pi rArr x = 0.1m`
aAlso speed of wave
`= (omega)/(k) = (50)/(10pi) = 5m//s` and `lambda = 2pi//k = 2pi//10pi = 0.2m`
Correct Answer – A::B::C::D