# Sound and Sensibility: Acoustics in Architecture, Music, and the Environment

## CONTENTS OF CURRICULUM UNIT 00.05.10

- Narrative
- Implementation
- The Nature of Sound
- The Features of a Sound Wave
- How Do We Hear
- How Does the Ear Detect the Source of a Sound?
- Sound In Intensity Level (Sound Pressure Levels)
- Acoustics in Architecture
- Lesson #1: The production of sound
- Lesson # 2
- Lesson #3
- Lesson # 4
- Suggested Readings
- Bibliography

### Unit Guide

## Discovering the Mathematics in Sound

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## Lesson # 2

Students should be familiar with the method by which sound waves are propagated. The feature of a longitudinal wave can be helpful in demonstrating amplitude, crest and trough of the wave. In addition, a slinky could be helpful in showing how the wave travels through the material. Students need to note the forward and backward movement of the coils as the disturbance or vibration moves from one point to the other with each section returning to its original position. This forward and backward movement represents one cycle. A repetition of this movement represents another cycle. The definition of frequency, f, could then be introduced as the number of times the wave goes through a cycle in one second (frequency, f, is the number of cycles completed in one second), measured in the unit of Hertz, Hz (1000 Hz = 1 kilohertz). What is one megahertz?

The time taken for the completion of one cycle is the period, (, in seconds. The distance on a wave from one crest to the next is called the wavelength, or the distance from one trough to the next (the wavelength determines the frequency of the wave).

The speed or velocity of a moving object is the distance traveled divided by the time it takes the object to move that distance. This is also referred to as rate (where velocity, v, is equal to the distance, d, divided by the time, (: c = d/().

In the case of a wave, the velocity, c, is equal to the wavelength, (, divided by the period, t (c = (/().

Examples: What is the velocity of a wave that has a wavelength of 10m and a period of 2 seconds?

Solution: c = (/(

c = 10/2 = 5 m/sec

If a wave has a period, (, of 0.01sec, what is the frequency, f ( frequency tells the number of cycles per second. We are given the information that in 0.01 seconds there was only one cycle). The task is to find how many cycles there are in one second.

Solution: f = 1/( and ( = 1/f

In the equation where c = (/(, it can also be expressed as c = ( f.

Since the speed of sound in air is a constant, 1100 feet per second, we can apply the formula to determine the wavelength if the frequency or the wavelength is known. Activity: What is my note?

Each student can measure his/her height in feet. This measurement should be used in the formula (c = (() to calculate the frequency. A chart with the frequency of the notes on the piano scale would be useful in assisting the student in identifying the particular key. The student should strike the key to acquaint himself/herself with that tone.