Question

A wave in a string has a wave function given by: y (x, t) = (0.0300m) sin [(5.35 m^-1) x + (1.63 s^-1) t]
  where t is expressed in seconds and x in meters. Determine:

a) the amplitude of the wave
b) the frequency of the wave
c) wavelength of the wave
d) the speed of the wave

Answer 1

for any given equation of wave in Y(x,t), all the parameters are specified already, you just have to work them out,

general equation of wave is given by Y(x,t) = A Sin (kxwt)

here,

A is the amplitude of the wave,

w is the angular frequency of the wave,

k is called as wave number,

k = w/v,

where v is the speed of wave,

we also know that,

v = f* , where is the wavelength of the wave

and w = 2f

therefore, k = 2/

now using the above formula and correlating it with the given equation;

a) amplitude = 0.0300m

b) frequency = w/2 = 1.63 / (2*3.14) = 0.2596 s^-1

c) wavelength : = 2* / k

= 2*3.14 / 5.35 = 1.1738 m

d) speed of wave = f* = 0.2596 * 1.1738 = 0.3047 m/s