Question

The transverse wave in a string is represented by y(x,t)=7.5sin(12π-0.005x) where x is in cm and t in second determine amplitude frequency wavelength velocity of wave

Answer 1

Answer:

A=7.5cm

frequency= 6

Wavelength= 4pie meter

Answer 2

The amplitude, wavelength and velocity of wave is 7.5 cm, 6 Hz and 7539.82 m/s respectively.

Explanation:

The transverse wave in a string is given by :

$y(x,t)=7.5\ \sin(12\pi t-0.005x)$...........(1)

the general equation of transverse wave is given by :

$y(x,t)=A\ \sin(\omega t-kx)$.........(2)

On comparing equation (1) and (2) we get :

Amplitude of the wave, A = 7.5 cm

$\omega=12\pi$

$2\pi f=12\pi$

$f=\dfrac{12\pi }{2\pi }$

Frequency, f = 6 Hz

Wavelength,

$k=0.005$

$\dfrac{2\pi}{\lambda}=0.005$

$\lambda=1256.5\ m$  

Velocity of the wave,

$v=\dfrac{\omega}{k}$

$v=\dfrac{12\pi}{0.005}$

v = 7539.82 m/s

So, the amplitude, wavelength and velocity of wave is 7.5 cm, 6 Hz and 7539.82 m/s respectively.

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