A wave of frequency 500 Hz has wave velocity of 350 m/s. 1)Find the distance between the two points which has $60^{o}$ $60^o$ out of phase. 2)Find the phase difference between two displacements at certain point of time $10^{- 3}$ $10^-3$ s apart?

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A wave of frequency 500 Hz has wave velocity of 350 m/s. 1)Find the distance between the two points which has $60^{o}$ $60^o$ out of phase. 2)Find the phase difference between two displacements at certain point of time $10^{- 3}$ $10^-3$ s apart?

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Answer 1 · 2017-06-01T02:32:45

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Given velocity of the wave $v = 350 m / s$ $v=350m"/"s$

frequency of the wave $n = 500 H z$ $n=500Hz$

So wave length of the wave $λ = \frac{v}{n} = \frac{350}{500} m = 0.7 m$ $lambda=v/n=350/500m=0.7m$

1) We are to find the distance between the two points which has $60^{\circ}$ $60^@$ out of phase i.e the phase difference is $ϕ = 60^{\circ} = \frac{π}{3} r a d$ $phi=60^@=pi/3 rad$

As we know that for path difference $λ$ $lambda$ there is phase difference $2 π$ $2pi$ ,

we can say , if $ϕ$ $phi$ is the phase difference for path difference $x$ $x$ ,then

$ϕ = \frac{2 π x}{λ}$ $phi =(2pix)/lambda$

$x = \frac{ϕ λ}{2 π} = \frac{π}{3} \times \frac{0.7}{2 π} = \frac{0.7}{6} m \approx 0.116 m$ $x =(philambda)/(2pi)=pi/3xx0.7/(2pi)=0.7/6m~~0.116m$

2) Now in $t = 10^{- 3} s$ $t=10^-3 s$ the wave moves

$v \times t = 350 \times 10^{- 3} = 0.35 m$ $vxxt=350xx10^-3=0.35m$

So here path difference $x = 0.35 m$ $x=0.35m$

So by the relation $ϕ = \frac{2 π x}{λ}$ $phi =(2pix)/lambda$ , the phase difference for $x = 0.35 m$ $x=0.35m$ becomes
$ϕ = \frac{2 π \times 0.35}{0.7} = π$ $phi =(2pixx 0.35)/0.7=pi$ ,

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A wave of frequency 500 Hz has wave velocity of 350 m/s. 1)Find the distance between the two points which has $60^{o}$ $60^o$ out of phase. 2)Find the phase difference between two displacements at certain point of time $10^{- 3}$ $10^-3$ s apart?

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A wave of frequency 500 Hz has wave velocity of 350 m/s. 1)Find the distance between the two points which has 60o60^o out of phase. 2)Find the phase difference between two displacements at certain point of time 10−310^-3s apart?

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A wave of frequency 500 Hz has wave velocity of 350 m/s. 1)Find the distance between the two points which has $60^{o}$ $60^o$ out of phase. 2)Find the phase difference between two displacements at certain point of time $10^{- 3}$ $10^-3$ s apart?