The transverse displacement $$\mathrm{y}(\mathrm{x}, \mathrm{t})$$ of a wave on a string is given by $$\mathrm{y}(\mathrm{x},\mathrm{t})=\mathrm{e}^{-(\mathrm{a}\mathrm{x}^{2}+\mathrm{b}\mathrm{t}^{2}+2\sqrt{\mathrm{a}\mathrm{b}}\mathrm{x}\mathrm{t}\}}$$. This represents a :
Given that $$y = e^{-(ax^2+2\sqrt{ab}xt+bt^2)} = e^{-(\sqrt{a}x+\sqrt{b}t)^2} = e^{-\sqrt{a}(x+\sqrt{\frac{b}{a}}t)^2}$$
The given displacement equation is of the form $$y = f(x+vt)$$
Thus, the wave moves in $$-\textrm{x}$$ with a speed of $$\displaystyle v = \sqrt{\frac{b}{a}}$$
A travelling harmonic wave is represented by the equation $$ y (x,t)=10^{-3}$$ $$\sin ({50t+2x) , } $$, where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave? The wave is propagating along the__?
Write the equation of the wave for a general time t, if the wave speed is v.
A transverse harmonic wave on a string is described by $$y(x,t) = 3$$sin $$(36t + 0.08x + \dfrac{\pi}{4})$$ where $$x$$ and $$y$$ are in cm and $$t$$ is in $$s$$. Which of the following statement incorrect?
Name the characteristic of the sound affected due to a change in its (a) amplitude (b) wave form (c) frequency.
Name the characteristic of the sound affected due to a change in its (a) amplitude (b) wave form (c) frequency.
The equation of displacement of two waves are given as $$y_1 = 10 \ sin (3\pi t + \pi /3)$$ $$y_2 = 5 \ (sin 3\pi t + \sqrt{3} cos 3 \pi t)$$, then what is the ratio of their amplitude;
The vertical displacement of the particle of the string at x = 7 cm and t = 0.01s will be