1. Sound Waves and Music
The Nature of a Sound Wave: Sound is a Mechanical Wave
A mechanical wave is a wave which is not capable of transmitting its energy through a vacuum.
Typically, this medium is air; though it could be any material such as water or steel.
There is an original source of the wave, some vibrating object capable of disturbing the first particle of the medium.
The sound wave is transported from one location to another by means of the particle interaction.

2. The Nature of a Sound Wave:Sound is a Longitudinal Wave:
The result of such longitudinal vibrations is the creation of compressions and rarefactions within the air.
Regardless of the source of the sound wave - whether it be a vibrating string or the vibrating tines of a tuning fork - sound is a longitudinal wave.

3. The Nature of a Sound Wave: Sound is a Pressure Wave
Sound is a mechanical wave which results from the longitudinal motion of the particles of the medium through which the sound wave is moving.

4. Sound Properties and Their Perception Pitch and Frequency
The frequency of a wave is measured as the number of complete back-and-forth vibrations of a particle of the medium per unit of time.
1 Hertz = 1 vibration/second
The diagram to the right shows two pressure-time plots,one corresponding to a high frequency and the other to a low frequency.

5. Sound Properties and Their Perception Pitch and Frequency
The ears of humans (and other animals) are sensitive detectors capable of detecting the fluctuations in air pressure which impinge upon the eardrum.
Any sound with a frequency below the audible range of hearing (i.e., less than 20 Hz) is known as an infrasound and any sound with a frequency above the audible range of hearing (i.e., more than Hz) is known as an ultrasound.

6. Sound Properties and Their Perception Pitch and Frequency
The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object.

7. Sound Properties and Their Perception Quality or timbre
The quality or timbre of the sound produced by a vibrating object is dependent upon the natural frequencies of the sound waves produced by the objects.

8. Sound Properties and Their Perception Pitch and Frequency
The tendency of one object to force another adjoining or interconnected object into vibrational motion is referred to as a forced vibration or resonance

9. Sound Properties and Their Perception Fundamental Frequency and Harmonics
resonance - when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.
(Note the length-wavelength-frequency relationship that was discussed earlier.)

10. Practice
1) Find the frequency of a sound wave moving in air at room temperature (speed at 20˚ C is 345 m/s) with a wavelength of m.
2) The human ear can detect sound with frequencies between 20.0 Hz and 16.0 kHz. Find the largest and smallest wavelengths the ear can detect. Temp. is 20˚ C
3) If you clap your hands and hear the echo from a distance wall 1.20s later, how far away is the wall. Temp. is 20˚ C

11. Ear Worksheet

12. Sound Properties and Their Perception Fundamental Frequency and Harmonics
Standing wave patterns are only created within the object or instrument at specific frequencies of vibration; these frequencies are known as harmonic frequencies, or merely harmonics.
Overtone- any frequency that is higher than the fundamental

13. Sound Properties and Their Perception Fundamental Frequency and Harmonics
The lowest frequency produced by any particular instrument is known as the fundamental frequency.
The fundamental frequency is alternatively called the first harmonic of the instrument.

14. Sound Properties and Their Perception Fundamental Frequency and Harmonics

15. Given: v = 425 m/s L = 76.5 cm = 0.765 m Find: f1 = ?? Diagram:
Practice Problem
The speed of waves in a particular guitar string is found to be 425 m/s. Determine the fundamental frequency (1st harmonic) of the string if its length is 76.5 cm.
The solution to the problem begins by first identifying known information, listing the desired quantity, and constructing a diagram of the situation.
Given:
v = 425 m/s
L = 76.5 cm = m
Find:
f1 = ??
Diagram:
      

16. Standing waves in air columns (pipes) Closed end pipes: Pipe open at one end.

17. Equation for closed end pipes Only odd Harmonics because at the open end there is always an antinode.

18. Closed pipe practice
Pipe is closed at one end, 1.50 m in length. If the speed of sound is 345 m/s, what are the frequencies of the first three harmonics that would be produced?

19. A sound wave traveling at 343 m/s is emitted by the foghorn of a tugboat. An echo is heard 3.00 s later. How far away is the reflecting object?
A stringed instrument has a maximum string length of 0.5 m and is tuned so that a wave travels along the string at 120 m/s. What is the string’s fundamental frequency at this length and wave speed?

20. Open End Pipes All Harmonics present

21. Open end pipes
fn= n v n = 1,2,3…. 2L

22. Open end (flute) practice
A pipe is 25 cm long and open at both ends. If the speed of sound is 345 m/s. What are the frequencies of the first three harmonics that resonate in the pipe?

23. If the wavelength of a 4. 40 x 104 Hz sound in freshwater is 33
If the wavelength of a 4.40 x 104 Hz sound in freshwater is 33.0 mm, what is the speed of sound in water?

24. The sound emitted by bats has a wavelength of 3. 5 mm
The sound emitted by bats has a wavelength of 3.5 mm. What is the sounds frequency in air? (Assume v = 345 m/s)

25. A boat sends a sonar signal down to the bottom of the ocean, the signal bounces off the bottom and the boat receives the 4.25 MHz signal back in 6.6 seconds. If the speed of sound in the water is 1452 m/s. How deep is the ocean?

26. When a tuning fork with a fundamental frequency of 392Hz is used with a closed-pipe resonator, the loudest sound is heard when the column is 21.0 cm. What is the speed of sound at this temperature?

27. Warm up
An upright wave moves to the right in a rope towards a boundary. The rope is connected to the wall with a nail. The wave then reflects off the boundary. Draw the entire situation and describe (use the following terms- upright, inverted, reflected, incident, wave)

28. Beats
Two sound frequencies that interfere constructively or destructively produce beats.
Fbeat = │f1 – f2 │
Two tuning forks, one with frequency of 442Hz, the other with frequency of 444Hz, are struck at the same time. What beat frequency will result?

33. Every 10 dB is 10 times more intense
The difference between 40dB and 50 dB is?
The difference between 40dB and 60dB is?
The difference between 40dB and 70dB is?

35. Palm pipes

36. How long
How long would an open pipe need to be in this room if its fundamental frequency is 392 hz?
How long would a closed pipe need to be in this room if its fundamental frequency is 392 hz?

37. A pipe has 110 hz, 220 hz, and 330 hz as its first three natural frequencies.
Is this an open or closed pipe?
If the pipe is 1.6 meters long, what is the temperature of the attic room in which the pipe is being examined?
What would be the wavelength of the 5th harmonic in this pipe?

38. A closed pipe is 0.60 meters long. The air temperature is 20ºC.
What is the fundamental frequency in the pipe?
What would be the frequency of the 2nd harmonic in this pipe?

39. The world's largest guitar, which was built by Indiana high-school students, can be played, although with strings that are 9.0 m long it is not an easy task. The fundamental vibration on each string has a wavelength equal to twice the string's length. Suppose the bass string makes a sound that has a frequency of 50.0 Hz. Find the speed of the wave in the string.

40. A group of swimmers are resting in the sun on an offshore raft
A group of swimmers are resting in the sun on an offshore raft. They estimate that 3 meters separate a trough and an adjacent crest of surface waves on the lake. They time the crests that pass by the raft and count 14 passing in 20 seconds. How fast are the waves moving?

41. A sound wave of wavelength 0
A sound wave of wavelength 0.70 m and velocity 330m/s is produced for 0.50 s.
a) What is the frequency of the wave?
b) After 0.50 s, how far is the front wave from the source of the sound?
c) How many complete waves are emitted in this time interval?