Question

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0700 m, and wavelength 0.320 m. These waves travel in the x  direction, and at t = 0 the x = 0 end of the string is at y = 0 and moving downward.

A. Find the frequency of these waves.

B. Find the period of these waves.

C. Write the equation for y(x,t) describing these waves.

D. Find the transverse displacement of a point on the string at x2 = 0.360 m at time t2 = 0.155 s .

Answer 1

v is the wave speed v = 8.00 m/s,

amplitude 0.0700 m = A

and wavelength 0.320 m = $\lambda$

A )

frequency = speed / wavelength

f = v / $\lambda$

f = 8 / 0.320

f = 25Hz

B )

time period of these waves is T

T = 1 / f

T = 1 / 25

T = 0.04 sec

C )

k = 2 $\pi$ / $\lambda$

k = 2 X 3.14 / 0.320

k = 19.625 m^-1

$\omega$ = 2 $\pi$ f

$\omega$ = 2 X 3.14 X 25

$\omega$ = 157 rad/s

y ( x , t ) = A X sin ( $\omega$ t - k x + $\theta$ )

y(x,t) = 0.0700 sin ( 157t - 19.625 x + $\theta$ )

for x = 0, and t = 0 and y ( x , t ) = 0

$\theta$ = 0

y ( x , t ) = 0.0700 sin ( 157 t - 19.625 x )

D )

x2 = 0.360 m at time t2 = 0.155 s .

y ( x , t ) = 0.0700 sin ( 157t - 19.625 x )

y ( x , t ) = 0.0700 sin ( 157 X 0.155 - 19.625 X 0.360 )

y ( x , t ) = 0.0700 sin ( 23.405 - 7.065 )

y ( x , t ) = 0.0700 X sin ( 16.34 )

y ( x , t ) = 0.0700 X 0.28133

y ( x , t ) = 0.0196 m