My Notes Ask Your Teach Transverse waves are being generated on a rope under con

Question

My Notes Ask Your Teach Transverse waves are being generated on a rope under constant tension. Determine the factor by which the required power is changed in each of the following situations (a) The amplitude is halved, and the angular frequency is doubled final/initial (b) Both the length of the rope and the wavelength are doubled. finalinitial (c) The angular frequency remains constant, and the length of the rope is doubled. finaVinitial1 (d) Both the wavelength and the amplitude are halved. final/initial1

Explanation / Answer

Here

average power in a transverse wave is given as

Pav = 0.25 * u*v * f^2* A^2/(4pi^2)

where u is the linear mass density

v is the speed of wave

A is the amplitude

now, a)

if A is halved and f is doubled , both effects cancel each other

final/initial = 1

b)

If wavelength is doubled , v will also double

hence , final/initial = 2

c)as there is no change in v or f

final/initial = 1

d)

wavelength is halved , this reduces the speed by half

A is also halved

final/initial = (1/2) * (1/2)^2

final/initial = 1/8

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