Two strings of different mass per unit length ${\mathbf{\mu }}_{\mathbf{1}}$and ${\mathbf{\mu }}_{\mathbf{2}}$are tied together and stretched with a tension F. A wave travels along the string and passes the discontinuity in ${\mathbf{\mu }}_{}$. Which of the following wave properties will be the same on both sides of the discontinuity, and which will change: speed of the wave; frequency; wavelength? Explain the physical reasoning behind each answer.

Tension on string linear mass density is equal to the wave speed.

Because each string's linear mass density is different, the wave's speed will be different as well.

As a result, the speed will vary.

The length of a wave is determined by its speed. When the speed of a wave increases, it means that the wave travels further in a given time interval than in the previous circumstance. It accomplishes this by increasing the wavelength. As a result, Wavelength will change.

The frequency of the wave would remain constant as it moved from one string to another with varied linear mass density. The reason is that as mass per unit length increases, wave speed decreases on decreasing the wavelength and vice versa.

$\mathrm{F}=\mathrm{v\lambda }$

Here, is the velocity and is the wavelength of the wave.

So, the frequency would remain the same.