sph3u – physics 11 university preparation – unit 4 – waves & sound created by: mr. d....

SPH3U – Physics 11 University Preparation – Unit 4 – Waves & SoundCreated by: Mr. D. Langlois – GECDSB – www.mrlanglois.wordpress.com

SPH3U - Unit 4

Waves & Sound


The Sound Barrier• As a source of sound increases in speed, the distance between the

compressions in the wavefront gets smaller. Once the source reaches the speed of sound, the distance between the compressions equals zero, and the compressions interfere constructively, producing an area of very dense, high pressure air – called the Sound Barrier.

• Unless the aircraft has been designed to cut through the sound barrier, there will be disastrous effects to the structure of the aircraft!

• At supersonic speeds, the spheres of the sound waves are left behind the aircraft. These interfere with one another constructively, producing large compressions and rarefactions along the sides of an imaginary cone extending behind the airplane. The intense acoustic pressure wave sweeps along the ground and is referred to as a Sonic Boom.


Sonic Booms


Mach Number

• A number indicating the ratio of the speed of an object to the speed of sound.

Mach Number = Vobject / Vsound

• Ex: Mach 1 = 344 m/s Mach 2 = 2 x 344 = 688 m/s

• M > 1 (Supersonic)• M = 1 (Speed of Sound)• M < 1 (Subsonic)


Example

• Calculate the Mach number of a Canadian Forces jet flying through 15 degrees C air with a velocity of 2.20x10^3 km/hr near Cold Lake, Alberta.


Practice

• Pg. 422 #1-3


Interference of Sound• When a tuning fork vibrates, a series of

compressions and rarefactions is emitted from outer sides of the tines, and from the space between them. Since the tines are out of phase, the compressions and rarefactions interfere destructively, producing nodal lines.


Interference of Sound

• Interference between two point sources, such as loud speakers is similar. Areas of constructive and destructive interference are located symmetrically about the midpoint of the pattern.

• If the loudspeakers are in phase there are areas of constructive interference where maximum sound intensity occurs. It is difficult to produce areas of total destructive interference because sound is reflected from the walls and other surfaces.



• Constructive Interference



• Destructive Interference


Noise-Canceling Head-phones• Destructive interference, if applied correctly, can be very

useful. It is very important that an airplane pilot hears what's going on around him, but engine noise presents a problem. So, pilots can use special headphones mounted with a microphone that picks up the engine noise.

• A component in the headphones then creates a wave that is the inverse of the wave that represents the engine noise. This wave is then played back through the headphones allowing destructive interference to produce a quieter background. Other applications for destructive interference are "quieting" rides in automobiles and passenger sections in airplanes.


Beats• When two waves with the same frequency

overlap, we have seen that the principle of superposition leads to constructive and destructive interference.

• Consider a point that receives sound waves of two slightly different frequencies. These waves arrive alternatively in phase and in opposite phase. This results in the loudness of the arriving sound to rise and lower periodically – faint, then loud, then faint, then loud, and so on.


Beats


Beats• A Beat is a full cycle of loudness variation

from loud to quiet and back to loud when two waves of different frequencies interfere.

• The number of beats that occur per second is known as the beat frequency:


Example

• Example: A tuning fork of unknown frequency is sounded simultaneously with a 512 Hz tuning fork. 20 beats are heard in 4.0s. What are the possible frequencies of the unknown fork?


The Physics of Tuning an Instrument

Musicians often tune their instruments by listening to a beat frequency. For instance, a guitar player plucks an out-of-tune string along with a tone that has the correct frequency. He then adjusts the string tension until the beats vanish ensuring that the string is vibrating at the correct frequency.


Vibrating Columns of Air• Musical instruments in the wind family depend on longitudinal

standing waves in producing sound. Since wind instruments (trumpet, flute, clarinet, pipe organ, etc) are modified tubes or columns of air, it is useful to examine the standing waves that can set up in such tubes.

• A column of air in a tube has a natural frequency. When an air column is vibrating at its natural frequency, there are standing waves in the tube. For example a tuning fork sends longitudinal waves down a tube which get reflected back at the other end. These longitudinal waves can be represented by a pattern which symbolizes the amplitude of the vibration. It is the greatest (antinode) where the pattern is the widest, and the smallest (node) where the pattern is the most narrow.


Vibrating Air Columns•A) Closed Air Column is closed at one end and open at the other. An antinode of the standing wave forms close to the open end creating a more intense sound. B) Open Air Column is open at both ends. An antinode forms at both ends.


Closed-end column (fixed frequency)

• Recall, two successive nodes or antinodes in a standing wave are 1/2λ apart. Therefore, the first resonant mode of vibration for a closed air column has a node at the closed end, and its adjacent antinode at the open end:

• ***The length of the first resonant mode of vibration is 1/4λ in a closed air column. ***


Closed-end column (fixed frequency)

• The second resonant mode is similar to the first, but now an additional node and antinode occur between the ends:

• The length of the second resonant mode is 3/4 λ in a closed air column.

• For the third resonant length, the column would be 5/4 λ. Clearly, there is a patter.

• The resonant lengths of a closed air column are odd integer multiples of the first resonant length 1/4 λ.


Example #1

• Example: What are the two lowest lengths of an air column, closed at one end, which would produce a 500Hz note when the air temp is 20◦C?


Open Air Columns (fixed frequency)• The resonant lengths of open air columns occur when the antinodes of

standing waves occur at Both ends of the column.

• The resonant lengths of an open air column are integral multiples of the first resonant length of 1/2 λ:


Example #2

• The second resonance length of an air column, open at both ends and resonating to a fixed frequency, is 64 cm. Determine the first and third resonance lengths.


Fixed Length Columns• In many cases, such as with instruments, the

length of the air column is fixed. A Bugle, for example has no valves, keys, or slides. How does the Bugler make sound?

• The pitch of a wind instrument can be changed not only by increasing/decreasing the column length, but also by increasing/decreasing the range of frequencies produced by the player’s lips.


Fixed Length Columns (open-end)


Fixed Length Columns

• Resonant frequencies of a fixed-length open air column are integral multiples of the first resonant frequency, f1.


Example #3

An air column, open at both ends, has a first harmonic of 330 Hz.

a) What are the frequencies of the second and third harmonics?

b) If the speed of sound in air is 344 m/s, what is the length of the air column?


Example #3 Solution

cmL

mL

L

L

vf

12.52

5212.0)2(330

3442

344330

21

b) We know the speed of sound and the fundamental frequency, so we can find the length of the column.


Fixed Length Columns (closed end)

• For a closed end column of fixed length,

• The resonance frequencies of a fixed length closed air column are odd-integer multiples of the first resonant frequency, f1.

fn = (2n – 1)f1

where f1 = V/4L


Example #4

4. An air column, closed at one end, has a first harmonic of 330 Hz. If the speed of sound in air is 344 m/s, what is the length of the length of the air column?


Practice

• Air Columns Worksheet #48-57

sph3u – physics 11 university preparation – unit 4 – waves & sound created by: mr. d....

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