Question

Sound waves and tuning forks

1. Why does the sound produced depend heavily on the orientation of the folk? This is referred’ directionally dependent’

2. How should you oriente the fork in order to best hear the sound it produces?

Answer 1

Frequency of Tuning Fork depends upon its material required to made it and ultimately on its dimession

Frequecy?dimession and material used

i.e.

Where-

f= Frequency of tuning fork in Hertz

l= length of pangs in meter

E= Young's Modules of material in Pascal

I= Second moment of inertia also called as area moment of inertia

?=density of material

A= area of cross section of pangs

If we keep E,? and l constant then we find that the frequency changes due to the ratio of I/A

Here I/A changes with the orientation along with the direction of motion

It is because of changing values of area moment of inertia

The formula can be seen like this also in terms of radius of Gyration(it is defined as the distance from the axis of rotation to a point where the total mass of the body is believe to be concentrated, so that the moment of inertia about the axis may remain unchanged )

Here for tuning fork value for K=?(t/12)

Therefore frequency of tuning fork is dependent upon radius of gyration. So greater the value of this will lead to greater the value of frequency.