Question

A certain transverse wave is described by y(x,t)=Bcos[2π(xL−tτ)], where B = 5.40 mm , L = 28.0 cm , and τ = 4.00×10−2 s . a)Determine the wave's wavelength. b)Determine the wave's speed of propagation

Answer 1

Transverse wave is given by:

y(x,t) = Bcos[2π(x/L − t/τ)] (There should be x/L and t/τ in your question please check this)

y(x,t) = Bcos[2x/L − 2*t/)]

Now compare it with standard equation:

y(x,t) = Bcos[w*x - k*t]

w = angular frequency = 2*/

= wavelength

from given expression

w = 2*/L = 2*/

= L = 28.0 cm

wavelength = = 28.0 cm = 0.28 m

Part B.

wave speed is given by:

wave speed = k/w = (2*pi/)/(2*pi/L)

wave speed = L/ = 0.28 m/(4.00*10^-2 sec)

wave speed = 7 m/sec