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Lab Exercise 6: Calculating the Speed of Sound

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  • Follow the instructions and directions below for this lab.  Disregard the outline in the manual for your LabPaq Kit.

  • Read this document entirely before starting your work.

  • Do not forget to record your measurements and partial results.

  • Submit a Laboratory Report through Moodle, as shown in the last section of this outline.  Remember that the Laboratory Report should include the answers to the questions below.

GOALS  

(1) to measure the speed of sound in air using the resonance of longitudinal waves

(2) to learn about sound and how it travels

(3) to learn how the speed of sound varies in different materials

(4) to learn about resonance and how to detect when it occurs

INTRODUCTION

Sound is a mechanical wave that is transmitted through solids, liquids, or gases. These waves are transmitted as a sequence of pressure changes which move through compressible media such as liquids and gases. The temperature and pressure of a substance can affect the speed of sound as these properties affect the density of the substance. Sound cannot travel through a vacuum. Due to physical differences among substances, sound travels at different speeds within different substances. Generally, the denser the material, the faster sound will travel through it. Solids have a high density, so sound travels faster in solids than in liquids or gases.

For example, on air (at 0° C), the speed of the sound is 331 m/s, while for air at 20° C its speed increases up to 341 m/s.  In water at 20°C the speed of sound is 1482 m/s and for granite, it is 6,000 m/s.

An accurate approximation of the speed of sound for air at different temperatures is given by the following equation, with t being the temperature of the air in degrees C:

Sound waves can be represented as shown in Figure 1.

The symbol λ is known as wavelength and represents the distance over which the wave repeats itself.  The number of repetitions of a wave during one second is known as frequency.  Frequency and wavelength are related with the following equation, with v being the speed of the sound, λ the wavelength, and f the frequency (frequency is also known as pitch).

Every object has a natural frequency at which it vibrates and is determined by its physical properties. This frequency is the object’s resonant frequency. When an object is exposed to waves that match or are very close to its resonant frequency, it will oscillate with increased amplitude. This effect is called resonance.

External forces such as earthquakes or musical instruments can cause the intensity of a material’s vibrations to increase. For instance, a trumpet can release sound waves that force a glass to vibrate. If these vibrations become large enough, the amplitude in the glass molecules can increase to a point that exceeds the plastic limit of the glass and it will shatter.

When sound waves with the same frequency approach each other from opposite directions, they interfere with each other. When these waves overlap, they form standing waves. Figure 2 shows an illustration of a standing wave. Note that the areas with the largest amplitude are called antinodes and the areas with the smallest amplitude are called nodes. Note also that two oscillations equal one wavelength as denoted by the bracket labeled “1.” When the waves overlap in such a manner that resonance occurs, this causes the amplitude to increase and thus results in a louder sound.

This resonance property will be used to determine the length of the wavelengths of sounds in this lab. A sound wave will be created by vibrating a tuning fork placed over the opening of a plastic (PVC) pipe. The sound waves will enter the pipe, hit the closed end, and bounce back to return to the opening. Because the frequency of the starting and returning waves will be the same, a standing wave similar to the one shown in Figure 2 will form.

As a plastic pipe partially submerged into a glass of water is raised and lowered, the ear detects the overlap of waves in a state of resonance as a louder sound coming from the pipe. The closed end of the tube contains a node which is the smallest amplitude of the wave and the open end contains an antinode which is the largest amplitude of the wave. Note in Figure 2 that the distance between any node and its adjacent antinode is λ/4.

The plastic tubing provided for this experiment will allow only the λ/4 measurement as the wavelength of the sound emitted by the tuning fork is approximately 1 m in length. In order to measure a full standing wave, a 1-m pipe would be required. If you have access to longer tubing, repeat the following procedure with this tubing.

PROCEDURE

In this lab we will find the wavelength of a certain frequency of sound emitting from a tuning fork.  Figure 3 shows this experimental setup for this lab.

Assume that this experiment is tested at an ambient temperature of 20° C, so the velocity for sound traveling in air is 343 m/s.  If you want to be more accurate, you can use the formula to estimate the speed of sound at other temperatures.

Fill a water glass, approximately 17 cm high, with tap water. The glass needs to be wide enough

to hold the plastic pipe.

Allow the tap water to equilibrate to ambient temperature. Use a thermometer to measure both the room temperature and the water; when they are the same temperature the water is equilibrated.

Figure 3: Experimental setup for determining the speed of sound

QUESTION 1

What is the temperature of the water once it has reached equilibrium with the air?  Transfer this number to the appropriate column in Table 1.

Place the plastic tube into the water.

QUESTION 2

What is the frequency of the tuning fork?  (This should be printed on the fork). Transfer this frequency to Table 1.

Hold the tuning fork by its handle and strike it against a wooden block or against the heel of your shoe.

Hold the vibrating tuning fork so that the tines are horizontally aligned near the top of the tube, but not touching the tube as shown in Figure 4.

Figure 4:   Vibrating fork

Move the tube slowly up and down in the water until the sound increases. At this point, the wavelengths are resonating.

At the point of the loudest sound, hold the pipe in place and use the tape measure to measure the distance from the top of the plastic tube to the top of the water. It might be helpful to have a partner measure this distance while you hold the pipe in place.  We will call this distance L for the equations that will be used.

QUESTION 3

What is the distance that results in the loudest sound?

Measure the inner diameter of the resonance tube.  Transfer your data to Table 1. Make sure that all your lengths are in meters.

Use the equation: λ = 4(L + 0.3d) , to solve for the wavelength of sound.

QUESTION 4

What is the calculated wavelength?  (Transfer this number to Table 1)

Using the following equation estimate the experimental measurement of the speed of sound:

QUESTION 5

What is the estimated measurement of the speed of sound?  (Transfer this number to Table 1).

Using the following equation, with t being the temperature of the air in degrees C, calculate the theoretical value for the speed of sound at the temperature of your experiment.

QUESTION 6

What is the theoretical speed of sound?  (Transfer your number to Table 1).

QUESTION 7

Calculate the % of error between the experimentally estimated and the calculated speed of sound.

QUESTION 8

Are you satisfied with your % of error that you achieved in this experiment?  If you, you may want to repeat this experiment with a different water recipient, etc. until you obtain numbers with which you are satisfied.

LABORATORY REPORT

Create a laboratory report  using Word or another word processing software  that contains at least these elements:

  • Introduction:  what is the purpose of this laboratory experiment?

  • Description of how you performed the different parts of this exercise.  At the very least, this part should contain the answers to questions 1-7 above.  You should also include procedures, etc. Adding pictures to your lab report showing your work as needed always increases the value of the report.

  • Conclusion: What area(s) you had difficulties with in the lab; what you learned in this experiment; how it applies to your coursework and any other comments.





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