As shown in the figure, a sinusoidal wave travels to the right at a speed of v1

Question

As shown in the figure, a sinusoidal wave travels to the right at a speed of v1 along string 1, which has linear mass density 1. This wave has frequency f1 and wavelength 1. Since string 1 is attached to string 2 (which has linear mass density 2 = 31), the first wave will excite a new wave in string 2, which will also move to the right.

a) What is the frequency, f2, of the wave produced in string 2? (Use the following as necessary: f1.)
f2 =

b) What is the speed, v2, of the wave produced in string 2? (Use the following as necessary: v1.)
v2 =

c) What is the wavelength, 2, of the wave produced in string 2? (Use the following as necessary: 1.)
2 =

Explanation / Answer

(a) Frequency depends on the source, but independent of the medium. So, frequency remains same. i.e. f 2 = f1 (b) Velocity is inversely proportional to the square root of linear mass density. v2 / v1 = (1 / 2 ) v2 = v1 * (1 / 31 )      = v1 / 3 (c) Velocity , v = f Hence, 2 / 1 = v2 / v1 [ since f is constant ]                         = 1 / 3 So, 2 = 1 / 3

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