Question

For the simple harmonic progressive wave Y=20sin2π(250t+x/20) Find amplitude a, angular velocity ω, wavelength λ​

Answer 1

Answer:

The answer is in the picture attached

Answer 2

Given:

Equation of progressive wave :

$y = 20 \sin2\pi(250t + \frac{x}{20} )$

To find:

• Amplitude
• $\omega$
• $\lambda$

Calculation:

General equation of a simple progressive wave:

$y = a \sin( \omega t + kx)$

Now, our given equation is :

$y = 20 \sin2\pi(250t + \frac{x}{20} )$

$\implies y = 20 \sin(500\pi t + \frac{\pi x}{10} )$

Now, compare with general equation:

• Amplitude = a = 20 metres

• $\omega$ = 500π rad/s

$\implies k = \dfrac{\pi}{10}$

$\implies \dfrac{2\pi}{ \lambda} = \dfrac{\pi}{10}$

$\implies \lambda = 20 \: m$

• So, wavelength = 20 metres