A light wire is tightly stretched with tension F. Transverse traveling waves of amplitude A and wavelength ?1 carry average power Pav,1 = 0.400 W. If the wavelength of the waves is doubled, so ?2 = 2?1, while the tension F and amplitude A are not altered, what then is the average power Pav,2 carried by the waves?
Solution 24E Step 1 of 5: The average power which is proportional to the square of the amplitude and angular frequency is given by, P avr= 1 F A2 2………..1 2 Where P avraverage power, F is restoring force(tension), is linear mass density , is angular frequency and A is amplitude. Step 2 of 5: In the given problem, the restoring force is tension force. Transverse waves on the light wire has initial amplitude A and wavelength 1arry power average P avr10.4 W. We need to calculate the average power carried P avr2when the wavelength is doubled; that is 2=2 b1 keeping tension force(F) and amplitude(A) constant. Step 3 of 5: To derive the relation between average power and wavelength, Using the fundamental relation, = vk 2 Substituting k= 2v = Where k is wavenumber, is wavelength , v is wave speed. Using this in equation 1 1 2v2 2 Pavr1= 2F( ) A …………..2