A traveling wave on a long string is described by the time-dependent wave function

f1(x,t)=a1sin(b1x−q1t),

with a1 = 5.00 × 10−2 m, b1 = 5π m−1, andq1 = 364 s−1 . You want a traveling wave of this frequency and wavelength but with amplitude0.0400 m, and you should add a second traveling wave to the same string in order to achieve this. Its wave function is

f2(x,t)=a2sin(b2x−q2t+ϕi).

Calculate the amplitude a2.

Calculate the wave number b2.

Calculate the angular frequency q2.

Calculate the smallest possible positive value of the initial phase ϕi.