Question

A wave pulse in a string is described by the equation $y_1=\frac{5}{(3x-4t{)}^2+2}$ and another wave pulse in the same string is described by $y_2=\frac{-5}{(3x+4t-6{)}^2+2}$. The values of $y_1,y_2$ and $x$ are in meters and t in seconds.
Which of the following statement is correct?

• A. $y_1$ travels along -x-direction and $y_2$ along + x-direction
• B. Both $y_1$ and $y_2$ travel along -x-direction
• C. Both $y_1$ and $y_2$ travel along + x-direction
• D. At $x=1m,y_1$ and $y_2$ always cancel
• E. At time $t=1s,y_1$ and $y_2$ exactly cancel everywhere

Answer 1

Answer: (D)

$\because$ Given,
$y_1=\frac{5}{(3x-4t{)}^2+2},y_2=\frac{-5}{(3x+4t-6{)}^2+2}$
According option (d), at $x=1$
$y_1=\frac{5}{(3-4t{)}^2+2}$
$y_2=\frac{-5}{(3+4t-6{)}^2+2}$
$=\frac{-5}{(3-4t{)}^2+2}$
Both wave pulse equation are existing in same string therefore resultant equation of wave pulse.
$y=y_1+y_2=0$