1. Chapter 12 Sound

2. The Origin of Sound  Sound is a longitudinal, mechanical wave.  You can hear sound with a frequency of 20 – 20,000 Hz. Under 20 hz is infrasonic, and above 20,000 hz is ultrasonic.  We talk about the frequency of sound when it is produced, and the pitch of sound when we hear it.

3. The Speed of Sound  The speed of sound depends upon the media in which it travels.  The speed of sound in air is 331 m/s at 0° Centigrade. V = 331 + (0.6 m/s/°C)T  The speed of sound increases by 0.6 m/s for every 1°C increase in temperature in air.

4. Loudness  When a sound is produced it has a certain intensity. This is defined as: I = Power/Area Area of the surface of a sphere 4 πr 2  Or intensity is measured as the ratio of power divided by the area when the sound is produced.  Loudness is a sensation when we hear a sound. Different people react differently to the same intensity. In other words the same level of sound has a different “loudness” to different people.

5. Intensity of Sound: Decibels  Intensity of sound, (I), is measured in W/m 2. However we often measure the loudness of a sound using a scale of relative intensity, known as the decibel (dB).  Decibels are a logarithmic scale which compares the intensity of a sound to the intensity of sound at the Threshold of Hearing, approximately 10 -12 W/m 2.  Hence the equation for calculating relative intensity is:

6. Sample Problem  What is the relative intensity, in dB, of a sound which has an intensity of 5 x 10 -10 W/m 2 ?

7. Solution

8. Forced Vibration and Natural Frequency  When a vibrating object is placed in contact with another object, the second object will also begin to vibrate. This is known as a force vibration.  An object’s natural frequency is one at which it takes a minimum energy to cause it to vibrate.  All object have a natural frequency at which they vibrate easily and if that frequency is within the range of human hearing – the object makes a sound.

9. Law of Pipes  For an Open Pipe (open at both ends) λ ≈ 2l or λ=2(l+0.8d)  For a Closed Pipe (open at one end) λ ≈ 4l or λ=4(l+0.4d)  In an open pipe all harmonics are present and in a closed pipe only the odd harmonics are present.

10. Sample Problem  If a pipe is 2 meters long at 0° C: What is its fundamental frequency and first two harmonics if it is:  Open  closed

11. Solution  Open pipe: λ≈2l = 2(2 m) = 4 meters f = V/λ = 330/4 = 82.5 Hz 2 nd Harmonic = 2(82.5) = 165 Hz 3 rd Harmonic = 3(82.5) = 247.5 Hz  Closed Pipe λ≈4l = 4(2 m) = 8 meters f = V/λ = 330/8 = 41.25 Hz 3 rd Harmonic = 3(41.25) = 123.75 Hz 5 th Harmonic = 5(41.25) = 206.25 Hz

12. Law of Strings  There are four laws which govern the frequency of a string: Length: Diameter: Tension: Density:

13. Sample Problem  A violin string has a frequency of 340 Hz when it is 1 meter long. What is its frequency when it is shortened to ½ meter?  When a guitar string is under a tension of 200 newtons it plays a frequency of 330 hz, what will it play if it is tightened to 450 newtons?

14. Solution

15. Interference  When two waves pass through each other they are said to form an interference pattern.  There are two types of interference pattern: Constructive interference  Waves reinforce each other Destructive interference  Waves cancel each other

16. Standing Waves  When a wave and its reflection reinforce each other they form a standing wave. In a standing wave the parts which don’t move are called nodes and the parts which move are called anti-nodes. Nodes are a results of destructive interference and anti-nodes come from constructive interference.

17. Beats  The beat frequency is an interference pattern which occurs when two frequencies are played at the same time.  The interference pattern has both constructive and destructive parts to it. The constructive parts cause a higher amplitude which is distinguishable from the frequencies being played. Hence a “beat pattern”  The number of beats/second is determined by taking the difference between the two frequencies being played.

18. Sample problem  If two tuning forks are struck, f 1 = 340 hz and f 2 = 364 hz, what beat frequency will be heard? Solution f b = f 2 – f 1 =364 hz – 340 hz = 24 hz or 24 beats/second

19. The Doppler Effect  When a person listening to a sound is moving and/or the source of the sound is moving you get the Doppler effect.  When they are getting closer together the sound that is heard is of a higher frequency than the original.  When they are moving apart, the sound that is heard is of a lower frequency than the original.

20. Doppler Effect: Moving Source- Stationary Listener  Source Approaching – Listener in Front  Source Moving Away – Listener Behind (Lb) V = speed of sound V s = speed of source

21. Sample Problem  A train has a whistle with a frequency of 330 Hz. If a listener on a platform hears the whistle as a train approaches the station at 40 m/s, what frequency does the listener hear?  The temperature is 20 °C.

22. Solution Speed of sound = 331 + (20 °C)(0.6 m/s/°C)

23. Doppler Effect: Moving Listener- Stationary Source  Listener Approaching – Listener Closing  Listener Moving Away – Listener Opening V = speed of sound V lc or V lo = speed of source

24. Sample Problem  A man is driving in his car, approaching a stationary siren with a frequency of 500 Hz. If he is traveling at 25 m/s, what frequency does he hear?

25. Solution Speed of sound = 331 m/s. Assume 0° C if not told otherwise.

26. Bow and Shock Waves  When a source moves as fast or faster than a wave in a media it creates a bow wave. If this is in air then the shock wave is three dimensional and is called a sonic boom.