Question

Q1 a long string of mass per unit length 0.2kgm^-1 is stretched to a tension of 500N.

(i) Find the speed of the transverse wave on the string

(ii) Find the mean power required to maintain a travelling wave of amplitude 10mm and wavelength 0.5m.

(iii) If the string is joined to another one of mass per unit length 0.8kgm^-1, what fraction of the power carried by the wave is transmitted tothe second string?

Answer 1

Q1

i)

= mass per unit length = 0.2 kgm^-1

T = tension force in the string = 500 N

speed of transverse wave on the string is given as

v = sqrt(T/) = sqrt(500/0.2) = 50 m/s

ii)

A = amplitude = 10 mm = 10 x 10^-3 m

= wavelength = 0.5 m

frequency is given as

f = v/ = 50/0.5 = 100 Hz

w = angular frequency = 2f = 2 (3.14) (100) = 628 rad/s

Mean power required is given as

P = (0.5) v A² w²

P = (0.5) (0.2) (50) (10 x 10^-3)² (628)²

P = 197.2 Watt