# waves and oscillations

### Measuring the speed of sound

In this experiment the speed of sound was measured through time of flight method using a sound card. Two microphones were placed a distance d apart, a ‘Pluck’ sound was then played from the computer and the signals received at each microphone were analyzed. The time delay between their initiation, which corresponded to the time taken for the sound to travel the distance was noted. The distance was varied with ten sets of readings taken at each distance to minimize uncertainty. The speed of sound was hence calculated by plotting a graph of ‘time delay’ vs ‘distance’ and taking its gradient. The recording, analysis and computation of data were all performed in MATLAB, the code for which was written by the students themselves.

This work has also resulted in a Task numbered 1.9 A for the Physics 100 course.

By Azeem Iqbal | Physics Studio

### Vibrations on a String and Resonance

1. Provided apparatus

2. Fixing a wooden support

3. Attaching string to the wooden support

4. Fixing a pulley

5. Measuring the diameter of a string

6. Connecting signal generator leads to the woofer

7. Woofer connected to the signal generator

8. Signal generator in frequency mode, AMPLITUDE OFFSET is 10V and BNC connector at the output knob

9. Attaching string to the woofer

10. Setup for finding the dispersion relation of a bare string

### Characteristics of Beverage Bottles as Helmholtz Resonators

It is a common phenomenon to observe that blowing over a glass beverage bottle produces a sound of a fairly definite frequency. The aim of this experiment was to see how well we could approximate glass bottles (such as that of a Sprite bottle) and a round bottom flask as ideal Helmholtz resonators in determining their fundamental frequencies and other associated harmonics. It was seen that though glass bottles are not Ideal Helmholtz Resonators, as they have no defined boundary between their neck and cavity, they can be assigned an average boundary level and then the approximation works to a fair degree of accuracy. In addition, a round bottom flask seems to, and can be approximated to a considerable degree, as an Ideal Helmholtz Resonator.

### Simple Harmonic Motion is Observed through Webcam

1. Provided apparatus

2. Webcam

3. A spring attached to the metre rule

4. Attaching a mass hanger to the spring

5. Adding weight in a mass hanger

6. Setup for observing free oscillations

7. Your M-files must be in the current directory of MATLAB

9. Placing mass-spring system into water

10. Setup for damped oscillations

11. Image view for damped oscillations

12. Cropped image view

13. Image processing view

This experiment involved analyzing the Chladni patterns both qualitatively and mathematically. Stationary waves were formed as the plate vibrates and produced exquisite patterns. The plate vibrated at its own modes of frequency. Since it was a two-dimensional plate, a particular mode was governed by two different numbers. These patterns follow the solutions of the wave equation. Simulations for both bounded and unbounded plates were performed using original codes written in Matlab to illustrate the various patterns formed.

Here is a video illustrating this astounding effect.