Question

The frequency of the transverse waves with an amplitude of 0.02 m moving along a + X axis with a speed of 10 m / s on a string is 5 Hz. Find the wavelength (λ) of the transverse waves traveling on this string and write the displacement equation of these waves. (Take = 3)

Answer 1

Wave is moving along a positive direction of X-axis.

Amplitude of the wave is $A=2\times 10^{-2}m$ .

Speed of wave is $v=10m/s$ ,Frequency is $\nu=5Hz$

Let, wave length of the given transverse wave is $\lambda$

We know that

$$v=\nu\lambda$$

Thus, on plugin the value we get

$$\lambda=\frac{10}{5}=2m$$

Wave equation is given by

$$y=A\sin(kx-\omega t)\\\implies y=A\sin\big(\frac{2\pi}{\lambda}x-2\pi\nu t\big)$$

Hence, on plugin the value we get our wave equation is

$$y=2\times 10^{-2}\sin(\pi x-10\pi t)$$