A wave represented by the given equation Y=Asin10 π x+15 π t+π3, where x is in meter and t is in second. The expression represents

Standard wave equation which travel in negative x-direction is y=A sin(ω t+kx+φ0)For the given wave ω=2πn=15π, k=2πλ=10πNow v=Co-efficient of tCo-efficient of x=ωk=15π10π=1.5m/secand λ=2πk=2π10π=0.2m

A wave represented by the given equation Y=Asin10 π x+15 π t+π3, where x is in meter and t is in second. The expression represents

Standard wave equation which travel in negative x-direction is y=A sin(ω t+kx+φ0)For the given wave ω=2πn=15π, k=2πλ=10πNow v=Co-efficient of tCo-efficient of x=ωk=15π10π=1.5m/secand λ=2πk=2π10π=0.2m

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A wave represented by the given equation $Y = Asin (10 π x + 15 π t + \frac{π}{3})$ , where x is in meter and t is in second. The expression represents

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A wave travelling in the positive X direction with a velocity of 1.5 m/sec

A wave travelling in the negative X direction with a velocity of 1.5 m/sec

A wave travelling in the negative X direction with a wavelength of 0.2 m

A wave travelling in the positive X direction with a wavelength of 0.2 m

answer is B, C.

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Detailed Solution

Standard wave equation which travel in negative x-direction is $y = A \sin (ω t + kx + φ_{0})$
For the given wave $ω = 2 πn = 15 π, k = \frac{2 π}{λ} = 10 π$
Now $v = \frac{Co-efficient of t}{Co-efficient of x} = \frac{ω}{k} = \frac{15 π}{10 π} = 1 .5 m / \sec$
and $λ = \frac{2 π}{k} = \frac{2 π}{10 π} = 0 .2 m$