The expression for y as a function of x and t for the given sinusoidal wave.

Question

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Answer 1

Question

Chapter 13, Problem 7P

(a)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave.

(a)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(0,t)$ is $0$ at $t=0$ .

The general expression for the sinusoidal wave is,

$y(x,t)=Asin(2πλx+2πft+ϕ)$ (I)

$y(x,t)$ is the transverse position of an element of the medium.

$A$ is the amplitude of the wave.

$λ$ is the wavelength.

$f$ is the frequency.

$ϕ$ is the phase.

Substitute $8.0 cm$ for $A$ , $80.0 cm$ for $λ$ and $3.0 Hz$ for $f$ in the above equation.

$y(x,t)=(8.0 cm×10−2 m1 cm)sin(2π80.0 cm×10−2 m1 cmx+2π(3.0 Hz)t+ϕ)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(0,t)=0$ at $t=0$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×0+6.0π×0+ϕ)0=sinϕϕ=0$

Substitute $0$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t)=0.08sin(2.5πx+6.0πt)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

(b)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.

(b)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(x,0)$ is $0$ at $x=10.0 cm$ .

Rewrite the equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(x,0)=0$ at $x=10.0 cm$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×(10.0 cm×10−2 m1 cm)+6.0π×0+ϕ)0=sin(0.25π+ϕ)0.25π+ϕ=0ϕ=−0.25π$

Substitute $−0.25π$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t−0.25π)=0.08sin(2.5πx+6.0πt−0.25π)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

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Answer 2

Question

Chapter 13, Problem 7P

(a)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave.

(a)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(0,t)$ is $0$ at $t=0$ .

The general expression for the sinusoidal wave is,

$y(x,t)=Asin(2πλx+2πft+ϕ)$ (I)

$y(x,t)$ is the transverse position of an element of the medium.

$A$ is the amplitude of the wave.

$λ$ is the wavelength.

$f$ is the frequency.

$ϕ$ is the phase.

Substitute $8.0 cm$ for $A$ , $80.0 cm$ for $λ$ and $3.0 Hz$ for $f$ in the above equation.

$y(x,t)=(8.0 cm×10−2 m1 cm)sin(2π80.0 cm×10−2 m1 cmx+2π(3.0 Hz)t+ϕ)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(0,t)=0$ at $t=0$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×0+6.0π×0+ϕ)0=sinϕϕ=0$

Substitute $0$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t)=0.08sin(2.5πx+6.0πt)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

(b)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.

(b)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(x,0)$ is $0$ at $x=10.0 cm$ .

Rewrite the equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(x,0)=0$ at $x=10.0 cm$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×(10.0 cm×10−2 m1 cm)+6.0π×0+ϕ)0=sin(0.25π+ϕ)0.25π+ϕ=0ϕ=−0.25π$

Substitute $−0.25π$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t−0.25π)=0.08sin(2.5πx+6.0πt−0.25π)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

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Answer 3

Question

Chapter 13, Problem 7P

(a)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave.

(a)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(0,t)$ is $0$ at $t=0$ .

The general expression for the sinusoidal wave is,

$y(x,t)=Asin(2πλx+2πft+ϕ)$ (I)

$y(x,t)$ is the transverse position of an element of the medium.

$A$ is the amplitude of the wave.

$λ$ is the wavelength.

$f$ is the frequency.

$ϕ$ is the phase.

Substitute $8.0 cm$ for $A$ , $80.0 cm$ for $λ$ and $3.0 Hz$ for $f$ in the above equation.

$y(x,t)=(8.0 cm×10−2 m1 cm)sin(2π80.0 cm×10−2 m1 cmx+2π(3.0 Hz)t+ϕ)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(0,t)=0$ at $t=0$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×0+6.0π×0+ϕ)0=sinϕϕ=0$

Substitute $0$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t)=0.08sin(2.5πx+6.0πt)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

(b)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.

(b)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(x,0)$ is $0$ at $x=10.0 cm$ .

Rewrite the equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(x,0)=0$ at $x=10.0 cm$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×(10.0 cm×10−2 m1 cm)+6.0π×0+ϕ)0=sin(0.25π+ϕ)0.25π+ϕ=0ϕ=−0.25π$

Substitute $−0.25π$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t−0.25π)=0.08sin(2.5πx+6.0πt−0.25π)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

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Answer 4

Question

Chapter 13, Problem 7P

(a)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave.

(a)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(0,t)$ is $0$ at $t=0$ .

The general expression for the sinusoidal wave is,

$y(x,t)=Asin(2πλx+2πft+ϕ)$ (I)

$y(x,t)$ is the transverse position of an element of the medium.

$A$ is the amplitude of the wave.

$λ$ is the wavelength.

$f$ is the frequency.

$ϕ$ is the phase.

Substitute $8.0 cm$ for $A$ , $80.0 cm$ for $λ$ and $3.0 Hz$ for $f$ in the above equation.

$y(x,t)=(8.0 cm×10−2 m1 cm)sin(2π80.0 cm×10−2 m1 cmx+2π(3.0 Hz)t+ϕ)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(0,t)=0$ at $t=0$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×0+6.0π×0+ϕ)0=sinϕϕ=0$

Substitute $0$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t)=0.08sin(2.5πx+6.0πt)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

(b)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.

(b)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(x,0)$ is $0$ at $x=10.0 cm$ .

Rewrite the equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(x,0)=0$ at $x=10.0 cm$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×(10.0 cm×10−2 m1 cm)+6.0π×0+ϕ)0=sin(0.25π+ϕ)0.25π+ϕ=0ϕ=−0.25π$

Substitute $−0.25π$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t−0.25π)=0.08sin(2.5πx+6.0πt−0.25π)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

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Answer 5

Chapter 13, Problem 7P

(a)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave.

(a)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(0,t)$ is $0$ at $t=0$ .

The general expression for the sinusoidal wave is,

$y(x,t)=Asin(2πλx+2πft+ϕ)$ (I)

$y(x,t)$ is the transverse position of an element of the medium.

$A$ is the amplitude of the wave.

$λ$ is the wavelength.

$f$ is the frequency.

$ϕ$ is the phase.

Substitute $8.0 cm$ for $A$ , $80.0 cm$ for $λ$ and $3.0 Hz$ for $f$ in the above equation.

$y(x,t)=(8.0 cm×10−2 m1 cm)sin(2π80.0 cm×10−2 m1 cmx+2π(3.0 Hz)t+ϕ)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(0,t)=0$ at $t=0$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×0+6.0π×0+ϕ)0=sinϕϕ=0$

Substitute $0$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t)=0.08sin(2.5πx+6.0πt)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

(b)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.

(b)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(x,0)$ is $0$ at $x=10.0 cm$ .

Rewrite the equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(x,0)=0$ at $x=10.0 cm$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×(10.0 cm×10−2 m1 cm)+6.0π×0+ϕ)0=sin(0.25π+ϕ)0.25π+ϕ=0ϕ=−0.25π$

Substitute $−0.25π$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t−0.25π)=0.08sin(2.5πx+6.0πt−0.25π)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Answer 6

Chapter 13, Problem 7P

(a)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave.

(a)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(0,t)$ is $0$ at $t=0$ .

The general expression for the sinusoidal wave is,

$y(x,t)=Asin(2πλx+2πft+ϕ)$ (I)

$y(x,t)$ is the transverse position of an element of the medium.

$A$ is the amplitude of the wave.

$λ$ is the wavelength.

$f$ is the frequency.

$ϕ$ is the phase.

Substitute $8.0 cm$ for $A$ , $80.0 cm$ for $λ$ and $3.0 Hz$ for $f$ in the above equation.

$y(x,t)=(8.0 cm×10−2 m1 cm)sin(2π80.0 cm×10−2 m1 cmx+2π(3.0 Hz)t+ϕ)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(0,t)=0$ at $t=0$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×0+6.0π×0+ϕ)0=sinϕϕ=0$

Substitute $0$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t)=0.08sin(2.5πx+6.0πt)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Answer 7

Chapter 13, Problem 7P

(a)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave.

Answer 8

(a)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(0,t)$ is $0$ at $t=0$ .

The general expression for the sinusoidal wave is,

$y(x,t)=Asin(2πλx+2πft+ϕ)$ (I)

$y(x,t)$ is the transverse position of an element of the medium.

$A$ is the amplitude of the wave.

$λ$ is the wavelength.

$f$ is the frequency.

$ϕ$ is the phase.

Substitute $8.0 cm$ for $A$ , $80.0 cm$ for $λ$ and $3.0 Hz$ for $f$ in the above equation.

$y(x,t)=(8.0 cm×10−2 m1 cm)sin(2π80.0 cm×10−2 m1 cmx+2π(3.0 Hz)t+ϕ)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(0,t)=0$ at $t=0$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×0+6.0π×0+ϕ)0=sinϕϕ=0$

Substitute $0$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t)=0.08sin(2.5πx+6.0πt)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave is $y(x,t)=0.08sin(2.5πx+6.0πt)$ .

Answer 13

(b)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.

(b)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(x,0)$ is $0$ at $x=10.0 cm$ .

Rewrite the equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(x,0)=0$ at $x=10.0 cm$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×(10.0 cm×10−2 m1 cm)+6.0π×0+ϕ)0=sin(0.25π+ϕ)0.25π+ϕ=0ϕ=−0.25π$

Substitute $−0.25π$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t−0.25π)=0.08sin(2.5πx+6.0πt−0.25π)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Answer 14

(b)

To determine

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.

Answer 15

(b)

Expert Solution

Answer to Problem 7P

The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

The value of $A$ is $8.0 cm$ , the value of $λ$ is $80.0 cm$ , the value of $f$ is $3.0 Hz$ and $y(x,0)$ is $0$ at $x=10.0 cm$ .

Rewrite the equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t+ϕ)$ (II)

Apply the condition $y(x,0)=0$ at $x=10.0 cm$ in equation (II).

$0=(0.08 m)sin(2.5π m−1×(10.0 cm×10−2 m1 cm)+6.0π×0+ϕ)0=sin(0.25π+ϕ)0.25π+ϕ=0ϕ=−0.25π$

Substitute $−0.25π$ for $ϕ$ in equation (II).

$y(x,t)=(0.08 m)sin(2.5π m−1x+(6.0π s−1)t−0.25π)=0.08sin(2.5πx+6.0πt−0.25π)$

Conclusion:

Therefore, the expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition is $y(x,t)=0.08sin(2.5πx+6.0πt−0.25π)$ .

Answer 20

Ch. 13.1 - (i) In a long line of people waiting to buy...Ch. 13.2 - Prob. 13.2QQ Ch. 13.2 - The amplitude of a wave is doubled, with no other...Ch. 13.3 - Suppose you create a pulse by moving the free end...Ch. 13.5 - Prob. 13.5QQ Ch. 13.7 - Consider detectors of water waves at three...Ch. 13.7 - Prob. 13.7QQ Ch. 13 - Prob. 1OQ Ch. 13 - Prob. 2OQ Ch. 13 - Rank the waves represented by the following...

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The expression for $y$ as a function of $x$ and $t$ for the given sinusoidal wave for given condition.