Resonances and wave speed: Set up the apparatus as shown in Figure $(2\mathrm{.}3).$ Connect the coaxial cable from the speaker to the OUTPUT of the function generator $($see the instructions at the end of this experiment$).$ The string should be hung with its knotted end inserted into the small yoke near the side of the speaker, passing through the yolk at the center and then on over the pulley at the end of the bench. A weight holder $($it has a mass of $50g)$ should be hung from the loop on the end of the string.

rigure $2\mathrm{.}3$ waves on a sung experimental setup

Add a $100g$ mass to the weight holder, for a total load mass of $150g,$ and set the string length to $70cm$ by measuring from the yoke at the centre of the speaker to the point where the string contacts the pulley.

$7$

Waves

Experiment $112-2$

Set the controls on the function generator as follows $($all other settings are arbitrary$)$:

FUNCTION Sine $()$ Wave

OUTPUT LEVEL Fully clockwise

RANGE $500$

COARSE FREQUENCY Fully counterclockwise

Set the controls on the function generator as follows $($all other settings are arbitrary$)$:

FUNCTION Sine $()$ Wave

OUTPUT LEVEL Fully clockwise

RANGE $500$

COARSE FREQUENCY Fully counterclockwise

FINE FREQUENCY Mid$-$range

Turn on the function generator, Rotate the COARSE FREQUENCY knob on the function generator while watching the vibrations on the string until you observe the string vibrating at its fundamental frequency. Fine tune the resonance by means of the FINE FREQUENCY knob, then record the resonant frequency directly from the function generator's display.

If the frequency generator is set at some simple fraction of the fundamental frequency $($e$.$g$.\frac{1}{2},\frac{1}{3},\frac{1}{2},$ etc.$)$ the string will still vibrate at its fundamental frequency. These frequencies are called sub$-$harmonics. How do you know whether the frequency is the fundamental or whether it is a sub$-$harmonic? The only way to find out is to double the frequency. Then, if the second harmonic is observed, you know that the original frequency was the fundamental. You should do this for the first data points in Part $2$ and Part $3.$

Determine the wavelength from the distance between the first and last node and the number of nodes $($refer to Fig. $2\mathrm{.}1).$ Then use equation $(2\mathrm{.}1)$ to calculate the wave speed.

Increase the frequency until you observe the second harmonic and again note the frequency $($fine tune it$)$ at which it occurs, and then calculate the wavelength and the wave speed. Continue this procedure for higher harmonics until it becomes too difficult to observe them.

What is the relationship between the fundamental frequency and the higher harmonic frequencies? Does the wave speed vary with frequency or is it a constant within the experimental errors?

I just want to know how the calculation work even its any number but an explain for every calculation

Figure $2\mathrm{.}3$ Waves on a String Experimental Setup

Add a $100g$ mass to the weight holder, for a total load mass of $150g,$ and set the string length to $70cm$ by measuring from the yoke at the centre of the speaker to the point where the string contacts the pulley.