P17_045.PDF

45. (a) Since the string has four loops its length must be two wavelengths. That is, λ = L/ 2, where λ is

the wavelength and L is the length of the string. The wavelength is related to the frequency f and

wave speed v by λ = v/f ,so L/ 2= v/f and L =2 v/f = 2(400m / s) / (600Hz) = 1 . 3m.

(b) We write the expression for the string displacement in the form y = y m sin( kx )cos( ωt ), where y m

is the maximum displacement, k is the angular wave number, and ω is the angular frequency. The

angular wave number is k =2 π/λ =2 πf/v =2 π (600Hz) / (400m / s) = 9 . 4m − 1 and the angular

frequencyis ω =2 πf =2 π (600Hz) = 3800rad / s. y m is 2 . 0mm. The displacement is given by

y ( x, t )=(2 . 0mm)sin[(9 . 4m − 1 ) x ]cos (3800s − 1 ) t .