# Labs from Chicago, Winter 1994 : Waves: Wavelength and Frequency.

Dr. Rich Kron, Dr. Heidi Newberg, and Luisa Rebull
Labs written for the CARA Space Explorers, Winter 1994

This is meant to be handed out to the students.

## Introduction

The purpose of this lab is to explore the concepts of wavelength and frequency and the connection between them. The other labs have involved learning about electronics. Light, radio waves, and television broadcasts are examples of electromagnetic radiation, which we characterize by wavelength and frequency of vibration. Instead of studying electromagnetic radiation directly, we will study another wave phenomenon, namely sound.

## Part 1. Measuring the Speed of Sound

The speed of sound depends on the medium - for example, sound travels much faster in water than it does through air (and it doesn't travel at all through a vacuum). We will measure the speed through air at conditions close to what is called Standard Temperature and Pressure (STP).

We will assume that light travels so fast that it is essentially instantaneous - a good approximation for our purposes. We will measure the speed of sound by the delay observed between the visible and audible manifestation of an event, such as a basketball being bounced on a sidewalk. The formula to calculate a speed or a velocity is

V = D / T ,

where V is the velocity, D is the distance traveled, and T is the time taken to travel that distance. To calculate V, obviously you need to measure D and T.

We'll do this lab outside in the Science Quadrangle if it is not raining; otherwise we will do it in the corridor of Kersten. One student will stand as far as is practical away from the others - at least a few hundred feet - and make a sound that is accompanied by an obvious visual cue (such as a dropped ball). The other students will observe this event (best using binoculars) and estimate the delay of the sound.

There are a number of ways to estimate the distance D. We will

leave it as an exercise for your group to devise a sensible method. To measure the time delay T, we will dribble the basketball with a regular frequency (bounces per second). This can be measured by counting the number of bounces in a minute, and dividing that number by 60. Suppose there is one bounce per two seconds (the frequency is 1/(2 sec), or 0.5 Hz), and that the observers hear the sound when the ball is half-way back up. This means that T is 0.5 sec in this case.

Record your team's values for D and T, and then calculate the speed of sound, V. What are the units for all of these quantities?

distance between sound origin and reception: ___________

time delay of sound wave: ___________

speed of sound: ___________

## Part 2: Tuning Forks, Frequency Generators, and Beat Frequency

Vibrating objects tend to emit sound at several frequencies. The most important one is usually the lowest, called the fundamental frequency. The others are called harmonics or overtones. Tuning forks are designed so that they emit sound at essentially one frequency only, namely their fundamental frequency. The note "A" has a frequency of 440 Hz, and the note "C" has a frequency of 263 Hz. These notes and their corresponding frequencies are usually marked on the tuning fork.

Pure tones can also be produced electronically with a gadget called a frequency generator. The ones we have in the lab have a digital read-out that tells you the frequency (in kilohertz). The output is sent both to a loudspeaker and to the oscilloscope.

Familiarize yourself with the oscilloscope. This equipment allows the "waveform" of the sound to be displayed, and thereby the frequency to be measured. If the horizontal display is set to 1 millisec per horizontal division, it means that a signal that has a frequency of 1000 hertz will show up as a complete wave in one division on the display. In this way, you can check the frequency displayed in the read-out of the frequency generator.

We can also verify the nominal frequency of a tuning fork by feeding the signal from a microphone into the oscilloscope.

nominal frequency ___________ Hz

number of divisions on oscilloscope _____________ div

time setting per division ________________ sec

derived frequency from oscilloscope ______________ Hz

If two sources have similar but not identical frequencies, you will hear a modulation in their combined sound called a "beat frequency." The closer the two frequencies, the smaller (lower) the beat frequency. If the higher-frequency tuning fork (or frequency generator) is vibrating at a frequency of f1 Hertz, and the lower- frequency tuning fork (or frequency generator) is vibrating at a frequency of f2 Hertz, then the beat frequency fb can be calculated from

fb = f1 - f2 (Hz).

Verify this formula by direct measurement using the oscilloscope of these three quantities.

f1 __________ (Hz).

f2 __________ (Hz).

fb __________ (Hz).

## Part 3. Vibrating Strings

Another well-known sound-producer is the vibrating string. The string has a certain length. It can vibrate in any of the ways shown in the sketch below. The first "mode" is normally the most important; this is the fundamental mode, and the others are the harmonics.

Note that the string itself forms a wave-like shape as it vibrates, and we can assign a wavelength to the vibrations on the string. Write down these wavelengths next to the sketch for the strings in the lab apparatus.

What does the sound of the string depend on? Verify that the sound depends on the following factors:

the tension in the string

the material the string is made out of

the length of the string.

Since you can change the note without changing the length of the string, it is clear that there is no direct connection between the wavelength of the vibration of the string, and the wavelength of the sound that the string emits. What matters is not the length of the string, but the frequency with which it is vibrating.

Tune one of the strings to the same note as one of the tuning forks. Since you know the frequency of the tuning fork, this allows you to assign the same frequency to the sound from the string.

frequency of vibrating string __________ (Hz)

## Part 4. Measuring the Wavelength of a Sound

There is a very important formula that relates the quantities of speed of a wave V, the frequency f, and the wavelength l (Greek letter lambda):

V = l x f .

If f is measured in Hertz and l is measured in centimeters, then the units of V will be cm/sec.

In Part 1 you measured V. In Part 4 you measured the frequency of the string by tuning it to the same frequency as the tuning fork. These data allow you to calculate the wavelength of the sound.

wavelength of the sound ____________ ( ).

If the frequency were higher, would the wavelength be the same, larger, or smaller?