Write the equation of the wave for a general time t, if the wave speed is v.

Open in App

Solution

According to the question,
At $t = 0, g (x) = A sin (x / a)$
Wave speed $= v$
$∴$ Time period , $T = a / v$ $(a =$ wave length $= λ)$
$∴$ General equation of wave
$y = A sin {(x / a) - t / (a / v)}$
$= A sin {(x - v t) / a}$

Suggest Corrections

Similar questions

A wave pulse is travelling on a string with a speed v towards the positive X-axis. The shape of the string at t = 0 is given by g(x) = $A s i n (\frac{x}{a})$ where A and a are constants. Write the equation of the wave for a general time t, if the wave speed is v.

Q. For the wave shown in the figure, write the equation of the wave if its position is shown at

t = 0

speed of wave is 200 m/s.

Q. For the wave shown in figure, write the equation of this wave if its position is shown at t = 0. Speed of wave is v = 30 m/s.

A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at $t = t_{0}$ is given by $g (x, t_{0}) = A s i n (\frac{x}{a})$ . Write the wave equation for a general time t.

Join BYJU'S Learning Program

Write the equation of the wave for a general time t, if the wave speed is v.

According to the question,At t=0,g(x)=Asin(x/a)Wave speed =v∴ Time period , T=a/v (a= wave length =λ)∴ General equation of wave y=Asin{(x/a)−t/(a/v)} =Asin{(x−vt)/a}

According to the question,
At $t = 0, g (x) = A sin (x / a)$
Wave speed $= v$
$∴$ Time period , $T = a / v$ $(a =$ wave length $= λ)$
$∴$ General equation of wave
$y = A sin {(x / a) - t / (a / v)}$
$= A sin {(x - v t) / a}$