A sinusoidal wave on a string is described by the equation y = (0.169 m) sin (0.713 x - 41.9 t), where x and y are in meters and t is in seconds. If the linear mass density of the string is 10.1 g/m ...

Question

a) ... the phase of the wave at x = 2.27 cm and t = 0.175 s. ?
b)... the speed of the wave ?
c)... the wavelength.
d) ... the power transmitted by the wave. ?

Answer 1

(a) Do you really mean x = 2.27 cm? Or should that be 2.27 m?
In either case, compute the value of
0.713 x - 41.9 t and divide it by 2 pi. Whatever is "left over" after the decimal point will tell you the phase, when compared to 2 pi.
(c) 0.713 m^-1 = (2 pi)/(wavelength)
wavelength = 8.81 m
41.9 s^-1= 2 pi f
f = 6.67 Hz
(b) speed = (wavelength)*(frequency)
= 58.75 m/s
(d) Wave pwer is proportional to frequency and Amplitude^2.

See the formula at
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/powstr.html

Answer 2

a) ... the phase of the wave at x = 2.27 cm and t = 0.175 s. ?
yes x is 2.27 cm. in meter is 0.0227m !

Answer 3

(d) Wave pwer is proportional to frequency and Amplitude^2.
f=6.669 Hz u=10.1 g/m
A=0.169 m
W=41.9
I tried with the power transmitted formula power=0.5*u*W^2*A^2*v
But my solution is wrong :(
I can not find a) and d) :(