Question

A sinusoidal wave travels down a long string. The y displacement of the string is given at right, as a function of both x position along the string and time t. Positions x and y are measured in meters, t is in seconds. Find the wavelength, frequency, and period of this waveform. y(x, t)=ysin(36.9t+2.43x)

If x is to the right, what direction is this wave traveling?

At time t = 0.0165 s, and a position x = 0.913 m, what is the phase of the wave?

Answer 1

given

y( x , t ) = y sin ( 36.9 t + 2.43 x )

time t = 0.0165 s

position x = 0.913 m

y( x , t ) = y sin ( 36.9 t + 2.43 x ) this equation can be comparing with the

following equation that is

y( x , t ) = A sin ( t + kx )

A = y ,

= 36.9 , k = 2.43

= 2 / T

36.9 = 2 / T

T = 1 / f

/ 2 = f

f = 36.9 / 6.28

f = 5.87 Hz

k = 2 /

= 2 / k

= 2 / 2.43 = 2.585 m

T = 1 / 5.87 = 0.17 sec

at time t = 0.0165 s and position x = 0.913 m

y ( 0.913 , 0.0165 ) = y sin ( 36.9 X 0.0165 + 2.43 X 0.913 )

y ( 0.913 , 0.0165 ) = y sin ( 0.6 + 2.21 )

y ( 0.913 , 0.0165 ) = y sin ( 2.81 )

y ( 0.913 , 0.0165 ) = 0.0490 m