Question

A transverse harmonic wave on a string is described by y(x, t)=3.0 sin (36 t +0.018 x + π/4) where x and y are in cm and tin s. The positive direction of x is from left to right: What are its amplitude and frequency?

Answer 1

standard equation of traveling wave is
$y(x,t)=asin(\omega t+kx+\theta)$
where a is the amplitude, $\omega$ is the angular frequency , k is wave number. e.g., k = 2π/wavelength. and $\theta$ phase constant.

compare both equations ,
we get, a = 3 so, amplitude of wave is 3cm

$\omega =36rad/sec$
we know, $\omega=2\pi\eta$
where $\eta$ is frequency .
so, 2π$\eta$ = 36
$\eta$ = 36/2π = 18/π=5.73Hz

$k=0.18$
so, 2π/wavelength = 0.018
wavelength = 2π/0.018 = 348.8cm

Answer 2

Answer:

Explanation:

Comparing with standard SHM equation,

y=Asin(wt+kx+ø)

where y is vertical displacement,

x is the horizontal displacement,

t is time,

ø is phase angle.

A is the amplitude.

So, amplitude=3cm

we know,

w=2πf,

where f is frequency.

So,we get the answer. Hope you understood.