The equations of two waves are given by :

y₁ = 5 sin 2$$\pi$$(x - vt) cm

y₂ = 3 sin 2$$\pi$$(x $$-$$ vt + 1.5) cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

The motion of a mass on a spring, with spring constant K is as shown in figure.


The equation of motion is given by
x(t) = A sin$$\omega$$t + B cos$$\omega$$t with $$\omega$$ = $$\sqrt {{K \over m}} $$

Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos($$\omega$$t $$-$$ $$\phi$$), where C and $$\phi$$ are :

A sound wave of frequency 245 Hz travels with the speed of 300 ms^$$-$$1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?