When a string is divided into three segments of length $$l$$₁, $$l$$₂ and $$l$$₃ the fundamental frequencies of these three segments are $${\upsilon _1},{\upsilon _2}$$ and $${\upsilon _3}$$ respectively. The original fundamental frequency ($$v$$) of the string is

Two identical piano wires, kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

Sound waves travel at 350 m/s through a warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air

Two waves are represented by the equations
y₁ = $$a$$sin($$\omega $$t + kx + 0.57) m and
y₂ = acos($$\omega $$t + kx) m, where x is in meter and t $$in$$ sec. The phase difference between them is