Two transverse sinusoidal waves travel in opposite directions along a string of length 3m whose both ends are fixed. The speed of transverse waves in the string is 0.5 cm/s. Each has an amplitude of 3 cm and wavelength of 6 cm. The equation for the resulting wave is

If the components waves are y1=asin(kx−ωt) and y2=asin(kx+ωt) then their superposition gives rise to a standing wave. If both ends of the string are attached to rigid boundaries, the equation of standing wave is y=2a sinkx.cosωt, such that at x = 0, y is zero for all values of t.Here, a=3cm, λ=6cm⇒K=2π6cm−1=π3cm−1Also, ωK=V⇒ω=0.5×π3 rads=π6 rads∴ The equation of resulting wave is y=6 sinπx3cosπt6option (1) is wrong as at x=0, y is not zero for all values of t.