Question

A trombone has a variable length. When a musician blows into the mouthpiece and causes air in the tube of the horn to vibrate, the waves set up by the vibrations reflect back and forth in the horn to create standing waves. As the length of horn is made shorter, what happens to the frequency?
A) The frequency will increase or decrease depending on how hard the horn player blows.
B) The frequency will increase
C) The frequency will decrease
D) The frequency will increase or decrease depending on the diameter of the horn.
E) The frequency will remain same

Answer 1

Answer:

B) The frequency will increase

Explanation:

The length of the instrument is given by

$L=\dfrac{\lambda}{2}\\\Rightarrow \lambda=2L$

Wavelength is given by

$\lambda=\dfrac{v}{f}$

$\dfrac{v}{f}=2L\ or\ L\propto \dfrac{1}{f}$

It can be seen that the length is inversely proportional to the frequency.

Here, the length of the trombone is decreasing so the frequency will increase.