[Physics Class Notes] on Measuring the Speed of Sound Pdf for Exam

The word “acoustic” is related to sound or the sense of hearing. It is a branch of sound that deals with understudies of mechanical waves in solids, liquids, and gases. These mechanical waves can be of sound, vibrations, ultrasound, and infrasound.

Since we are dealing with sound waves, so we will talk about Acoustic Sound. Sound travelling in the form of waves has some speed that can be in m/s, kmph, and mph. 

Speed of sound is the distance travelled by a unit wave through the air/elastic medium carrying various units of measurement. 

On this page, you will find multiple units of sound with the experiment to measure speed of sound in air.

Important Point:

In the 17th century, the French scientist and philosopher Pierre Gassendi is known to be the dist to attempt the measuring the speed of sound in air.

Speed of Sound in Air

For measuring the speed of sound, we need to measure the distance it covers through the medium.

For instance, the speed of sound in meters per second (in dry air) is 343 meters per second; however, this velocity value is considered at a temperature of 20 ⁰C (68 ⁰F).

Moving forward, the speed of sound is measurable in various media and units like we discussed for m/s (m/s = SI unit of speed).

Now, let’s discuss the speed of sound in miles per hour, speed of sound km per hour,  and how the experiment for the determination of the speed of sound can be performed:

Speed of Sound in Various Units

The speed of sound is measured in the following units:

• Speed of sound in Km per hour      –     1,235 Kmph

• Speed of Sound in miles per hour   –      767 mph

• Speed of sound in air feet per second      –      1,125 ft s⁻¹

The velocity of sound is measured in hydrogen and oxygen (H2 and O2) is always 332 m/s.

Before starting with the experiment to measure the speed of sound, we must know the sound measurements symbols:

Measuring the Speed of Sound in Air

Point to Note:

The speed of sound strongly depends on the temperature and the medium through which it propagates.

Do You Know the Speed of Sound is Measured by Which Instrument?

We can measure the speed of sound by using an oscilloscope, a square-wave oscillator, and a piezo-electric pick-up. 

A study of the connection between the space travelled, and therefore, the time of arrival of the sound wave allows a graphical determination of the speed of the heartbeat within the lucite rod.

Now, let us understand the experiment to measure speed of sound in air:

Experiment to Determine the Speed of Sound

Theory 

In 1866, August Kundt first described this experiment. In this context, we will be performing a common experiment in physics. The acoustic tube is also known as the Kundt’s tube.

Aim of this Experiment:

This experiment aims to measure the speed of sound “c” in air, or other gasses, by observing standing acoustic waves in a tube. 

 

Do You Know?

We can determine the speed of sound in the air by using a smartphone and a cardboard tube.

However, for making the experiment economical/affordable in terms of equipment. We are measuring the speed of sound within 3% of the theoretical prediction.

Theory of the Experiment:

Now, start with the theoretical part:

We place the smartphone such the microphone is found within the opening of the tube. this is shown in the figure below:

The phone is about to record audio with a frequency of 44.1 kHz. During the phone recording, the function generator app emits a pure wave. 

The wave traverses a path from 50 Hz to 3000 Hz at a rate of 1 Hz s−1. The sound recording is stored in .wave format. This format makes for straightforward data analysis later.

For a sinusoidal wave with constant frequency f  and wavelength, propagating in a medium, the speed of sound in the said medium is given by:

           c  =   fλ

On determining the wave’s frequency and wavelength, we can measure the speed of sound in the medium. 

When an acoustic wave enters through the open end of a half-closed tube and hits the closed-end, part of the wave is reflected towards the tube’s opened end. At specific wavelengths, the incident and the reflected wave form a standing wave. 

In the antinodes of the standing wave, the points on the standing wave where the amplitude is maximum, the amplitude of the standing wave is greater than the amplitude of the incident wave.

The displacement antinode of the standing waves is the opening of the tube. The resonance wavelengths are the wavelengths at which the standing waves occur.

For the half-closed tube, the resonances occur when the tube’s length equals an odd number of quarter wavelengths of the incident wave:

                       λn  = 4L/n,  

Where

  n  =  1, 3, 5,….

Here,

“n” is the nth harmonic of the tube

L is the length of the tube.

The resonance frequencies fn of the tube, the frequencies at which standing waves occur in the tube, can be found by combining both equations:

                                λn  = 4cL/n, 

Where

n  =  1, 3, 5,…..

Result:

Frequencies at peak amplitudes: