Answer
(a) Increasing the tension will increase the wave speed in the string, which in turn increases the frequency.
(b) Changing the length of the string will change the wavelength, which in turn changes the frequency.
(c) A different string could have a different tension or a different mass per length, which will result in a different wave speed along a different string. Changing the wave speed will change the frequency.
Work Step by Step
(a) We can write an equation for the wave speed in the string:
$v = \sqrt{\frac{T}{m/L}}$
Increasing the tension will increase the wave speed.
We can write an equation for the frequency:
$f = \frac{v}{\lambda}$
Increasing the wave speed will increase the frequency.
(b) We can write an equation for the wavelength of the fundamental standing wave:
$\lambda = 2L$
Changing the length of the string will change the wavelength.
We can write an equation for the frequency:
$f = \frac{v}{\lambda}$
Changing the wavelength will change the frequency.
(c) We can write an equation for the wave speed in the string:
$v = \sqrt{\frac{T}{m/L}}$
A different string could have a different tension or a different mass per length, which will result in a different wave speed along a different string.
We can write an equation for the frequency:
$f = \frac{v}{\lambda}$
Changing the wave speed will change the frequency.
