A Sound wave with an amplitude of $3 c m$ starts moving towards right from origin and gets reflected at a rigid wall after a second. If the velocity of the wave is $340 m s^{- 1}$ and it has a wavelength of $2 m$ , the equations of incident and reflected waves are

y = 3 \times 10^{- 2} sin π (340 t - x), y = - 3 \times 10^{- 2} sin π (340 t + x)

towards left

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y = 4 \times 10^{- 2} sin π (340 t + x), y = - 4 \times 10^{- 2} sin π (340 t + x)

towards left

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y = 5 \times 10^{- 2} sin π (340 t - x), y = - 5 \times 10^{- 2} sin π (340 t - x)

towards left

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y = 6 \times 10^{- 2} sin π (340 t - x), y = - 6 \times 10^{- 2} sin π (340 t + x)

towards left

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Solution

The correct option is A $y = 3 \times 10^{- 2} sin π (340 t - x), y = - 3 \times 10^{- 2} sin π (340 t + x)$ towards left
$A = 3 c m$
$y = A sin (V t - x)$
$V = λ / t$
$f = 170 s e c$
$y_{1} = A sin (V t - x)$
$y_{2} = A sin (V t + x)$
$∴ y_{1} = 3 \times 10^{- 2} sin k (340 t - x),$
$y_{2} = 3 \times 10^{- 2} sin k (340 t + x)$
$k = \frac{2 π}{λ}$
$k = \frac{2 π}{2}$
$k = π$
$∴ y_{1} = 3 \times 10^{- 2} sin π (340 t - x)$
$y_{2} = 3 \times 10^{- 2} sin π (340 t + x)$

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A Sound wave with an amplitude of 3cm starts moving towards right from origin and gets reflected at a rigid wall after a second. If the velocity of the wave is 340ms−1 and it has a wavelength of 2m, the equations of incident and reflected waves are

The correct option is A y=3×10−2sinπ(340t−x),y=−3×10−2sinπ(340t+x) towards leftA=3cmy=Asin(Vt−x)V=λ/tf=170secy1=Asin(Vt−x)y2=Asin(Vt+x)∴y1=3×10−2sink(340t−x),y2=3×10−2sink(340t+x)k=2πλk=2π2k=π∴y1=3×10−2sinπ(340t−x)y2=3×10−2sinπ(340t+x)

A Sound wave with an amplitude of $3 c m$ starts moving towards right from origin and gets reflected at a rigid wall after a second. If the velocity of the wave is $340 m s^{- 1}$ and it has a wavelength of $2 m$ , the equations of incident and reflected waves are