CBSE Class 12-science Answered

General equation for progressive wave travelling  is

y(x,t) = A sin[ (2π/λ) x ± (2πf ) t ) .....................(1)

where A is amplitude , λ is wavelength and f is frequency .

+ sign is for the wave traveling in -x axis direction

- sign is for the wave travelling in +x axis direction.

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Given wave equation is

y(x, t ) = 0.5  sin ( 2π t + 2π x ) 

hence amplitude is 0.5 unit , frequency is 1 Hz. and  wave is travelling in -x axis direction

if amplitude is doubled new amplitude is 1 unit .

If frequency is halved , new frequency is (1/2) Hz.

If wave is travelling in opposite direction, then direction of propagation is along +x axis .

If the medium is same then velocity of wave is constant . velocity of wave is product of frequency and wavelength .

Hence if frequency is halved , then wavelength is doubled .

Then equation for new wave is

y(x,t) = 1.0 sin ( π x - π t )