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 )