An oscillator creates periodic waves on two strings made of the same material. the tension is the same in both strings.

if the strings have different thicknesses, which of the following parameters, if any, will be different in the two strings?
-wave frequency
-wave speed
-wavelength
-none of the above

if the strings have the same thickness but different lengths, which of the following parameters, if any, will be different in the two strings?
-wavelength
-wave speed
-wave frequency
-none of the above

1. -none of the above

First of all, we have to notice that the speed of a wave in a material depends only on the properties of the material: therefore, if we use two strings made by the same material, the wave speed in the two strings will be the same.

Secondly, we can observe that the fundamental frequency of a wave on a string is given by

where

L is the length of the string

T is the tension in the string

is the linear density of the string, with m being its mass

In this problem, the only difference between the two strings is in the thickness. Therefore, since the two strings have same length (L), same tension (T) and same linear density (), their frequency is the same.

And lastly, since the wavelength is given by the equation

where v is the wave speed and f is the frequency, since both v and f do not change, then the wavelength in the two strings is also the same.

2. wavelength  and wave frequency

As before, the two strings are made of same material, so they have same wave speed.

The frequency instead is given by

and since this time the two strings have different length L, then they also have different frequency.

And then, from the equation

we also conclude that if the frequency changes and the wave speed remains the same, then the wavelength must change as well.

i would think it's food chain