The equation of wave prodeced in a string with both the end fixed is y = cos⁡ 2πt sin ⁡2πx. Then what is the minimum length of the string?

Least length of a vibrating clamped string will be obtained when one loop is formed in the string. In that case, we have:λ2=l …(i)Also,λ=2πk( k is the wave number, it is the coefficient of x in a wave equation)λ=2π2π=1m(∵k=2π)∴l=12= Minimum length  (from (i))