Chapter 8: Wave and Sound

Which of the following diagrams represents the softest sound?

C. Because it has the smallest amplitude and wavelength

In a liquid such as water the speed of sound at 19o C is 1461 meters/second approximately four to five times faster than air.

In some solids, the speed of sound is even greater, for example: in iron, sound may travel 5,000 meter/second, about 15 times faster than air. The speed of sound in various substances can be seen in the following chart.

Sound waves are given off in all directions from a vibrating body. If they travel through a uniform medium, they spread out in a spherical pattern. Thus, the area of the expanding wave front is increasing in proportion to the square of the distance from the source.

Since the total energy of the wave is constant, the intensity of the wave diminishes as it moves away from the source. The sound waves produced by a whistle are only one-fourth as intense at a distance of two kilometers as they are at a distance of one kilometer from the source

What is the wavelength of a sound resonating in a closed tube 105 cm long?

Wavelength: λ = 4 x length λ = 4 x 105 Cm 420 cm

What is the wavelength of a sound resonating in a closed tube 10 cm long?

Wavelength: λ = 4 x length λ=4 x 10 cm 40 cm

Sound may be specifically defined as

a mechanical vibration in a material medium (solid, liquid, gas) within a frequency range approximately between 20 waves/s and 20,000 waves/s. One wave/s is 1 Hertz (Hz). These frequencies are capable of affecting the human ear (providing that its intensity is between 0 db and 120 db). Waves of frequencies lower than 20 Hz are called infrasonic, and those of frequencies higher than 20,000 Hz are known as ultrasonic.

Matter that is vibrating produces

sound

Waves possess five basic characteristics.

1. Wavelength (λ), is the distance from a point on a wave to the next point 2. Amplitude (A), is the maximum displacement (distance) of any wave. Amplitude indicates the loudness of a sound. 3. Period (t), is the time (usually expressed in seconds) that it takes for a wave to travel one full wavelength. 4. Frequency (f), is the number of vibrations (waves) occurring in one second of time. This indicates the pitch of a sound. 5.Wave speed (v), is the rate the wave is traveling; the units of measurement are meters/s

What is the velocity of a sound whose wavelength is 3.0 cm and whose frequency is 1235 Hz?

1. Wavelength (λ), is the distance from a point on a wave to the next point 2. Amplitude (A), is the maximum displacement (distance) of any wave. Amplitude indicates the loudness of a sound. 3. Period (t), is the time (usually expressed in seconds) that it takes for a wave to travel one full wavelength. 4. Frequency (f), is the number of vibrations (waves) occurring in one second of time. This indicates the pitch of a sound. It needs to be in meters so 3.0 cm needs 0.030 M Speed of Sound: v = f x λ 0.030*1235 Hz=37.2 =37 m/s

Model of Sound Suppose you take a very thin strip of wood or a piece of steel like a hacksaw blade and clamp one end in a vise. If you strike this clamped material sharply, the free end would vibrate back and forth. If you cause the wood or steel to vibrate rapidly, it would produce a humming sound that could be heard. You could do other experiments, such as the plucking of a guitar string, or the striking of a fork, which show that sounds are produced by vibrating matter.

As the vibrating strip moves forward it moves the gas molecules compressing them thus transferring mechanical energy to the molecules in the direction in which the compression occurs. At the same time, the gas molecules on the other side of the strip expand into the space left behind the strip, and they become more separated or rarefied. The combined effect of the simultaneous compression and rarefaction transfers energy to the molecules in the direction of the vibration of the strip. The type of wave produced as this mechanical process continues is called a longitudinal wave. Figure 1 Waves possess five basic characteristics. Figure 2.

A person is standing near a reflecting surface. He shouts, and hears an echo 10 seconds later. If the temperature is 25o C how far is he from the surface?

Find Vt first so, 330 m/s+(.6 m/s*25 C)=15+330 m/s=345 m/s Distance from reflecting surface X=(Vt * t)/2 X=(345 m/s*10)/2=3450/2= 1725 m

A person shoots a gun near a reflecting surface. The same person hears the echo 7 seconds after the shot. If the temperature is 40oC, how far is the person from the reflecting surface?

Find Vt first so, 330 m/s+(.6 m/s*40c)= 24+330=354 m/s Distance from reflecting surface X=(Vt * t)/2 x=(354 m/s *7)/2=2478/2= 1239 m

By investigating the relationship between frequency (vib/s) and wavelength (m/vib) one would observe that if they are multiplied together and we cancel appropriate units the results would be units of (m/s).

Frequency *wavelength =velocity Cancel out vibration Cancel out vibration (vibration/second) * (meters/vibration) =meters/second Since the tuning forks are stamped with their frequency (f) and the wavelength () can be obtained through resonance we can calculate the velocity of sound in the classroom

Frequency

Frequency is what we perceive as a note played by a instrument. We would consider the note to be of a high pitch or a low pitch. Frequency is the number of waves per second measured in Hertz. As the frequency, or number of waves per second, increases the wavelength decreases. As the frequency of a sound decreases the wavelength increases

The loudness of a sound at any point can be measured using a relationship referred to as the The interesting thing about this law is that it describes the energy of various forms of energy

Inverse Square Law.

The model of sound contains two fundamental characteristics, loudness and frequency.

Loudness is indicated by the height or amplitude of the wave. The frequency or pitch is indicated by the number of waves drawn in a given distance

What is the velocity if the wavelength is 4 meters, and the frequency is 282.5 Hz?

Speed of Sound: v = f x λ 1130 m/s = 4 m*282.5 hz

Characteristics of Sound 1 Interference

The concept of waves is not unique to sound. For instance, if you drop a rock into a pond, waves will be produced. These waves can overlap, and in overlapping, some of the effects of the waves may be increased, decreased, or neutralized. As the crest of one wave overtakes the crest of another, the affects combine. The result is a wave of increased amplitude. This is called constructive interference, or reinforcement. By the same token, when the crest of one wave overlaps the trough of another, their individual affects are reduced. The high part of one wave simply fills in the low part of another. This is called destructive interference, or cancellation. These concepts transfer neatly from the rock in the water example described above to the fundamental concepts of sound.

Loudness

The loudness of a sound depends on the affect (as indicated in our model by amplitude) of the sound waves on the ears. In general, sound waves of higher amplitude or intensity are louder. The ear is not equally sensitive to sound of all frequencies. Consequently, a high frequency sound may not seem as loud as one of lower frequency having the same intensity. An increase in the intensity of a sound of fixed frequency, while the observer remains at a fixed distance from its source, causes the sound to seem louder. However, the relation between intensity and loudness is not a one-to-one relationship. For example: sound must be ten times more intense before it becomes twice as loud; and 100 times as intense before it becomes three times as loud. Intensity is measured with acoustical apparatus, and does not depend on the sense of hearing of an observer. (see figure 6 for examples)

Characteristics of Sound 3 Speed of Sound The speed of sound in the air is about 330 meter/second at 0o C. As the temperature of the air rises, the speed of sound increases, at a rate of about 0.6 meter/second for each Co. The formula or relationship can be stated as:

VT = 331 m/s + (.6 m/s 0C x T) It must be noted this formula works only for sound traveling in air. The temperature must be in units of oC. The unit for the speed of sound is m/s.

Given the air temperature 21o C, calculate the speed of sound

VT = 331 m/s + (.6 m/s 0C x T) VT=331m/s+(.6 m/s *21o)=343.6 VT=343 m/s round up

What is the speed of sound at 45o C?

VT = 331 m/s + (.6 m/s 0C x T) VT=331m/s+(.6 m/s *45o)=331+27=358 VT=358 m/s

Characteristics of Sound 2 Doppler Effect

When a sound is moving with respect to the observer the sound's pitch appears to change. Because of the motion of the source, illustrated here as a racing car, the sound waves appear to be bunched up in front and spread out in back. This results in shorter wavelengths, or an increased frequency, in the front of the source and longer wavelengths, or a lower frequency behind the source.

Resonance You may have noticed that a person singing or a sound from the radio or television can cause some object in the room to vibrate. This is referred to as resonance. (Is it live, or is it Memorex?) Resonance occurs when the natural rates of vibration of two objects are the same. If you hold a vibrating tuning fork over a plastic cylinder as shown in the Figure, you can observe resonance. You will need to adjust the length of the tube by moving it up and down, until the sound produced seems the loudest. The following paragraph and Figure will explain how the sound becomes louder.

When a vibrating tuning fork is in the 'down' position (b), the sound wave travels down the tube, reflects off the water, and returns to the tuning fork, just as it reaches the 'up' position (a). The reflected sound reinforces the sound made by the tuning fork, making it seem louder. The sound has gone down the length of the tube (L) and back; or 2L, in half of a wavelength, (distance a to b). The length of the tube is half a wavelength divided by 2, or 1/4 wavelength. The length of the tube is one quarter of the wavelength of the sound being produced. To determine the wavelength of the sound produced multiply the length of the tube by four. This relationship can be expressed as: λ = 4 x L.

The power of sound (as judged by the ear. is represented by

amplitude

A and B, respectively, are:

amplitude (the maximum displacement (distance) of any wave. Amplitude indicates the loudness of a sound.) and wavelength (the distance from a point on a wave to the next point)

Decibel Levels decibel meter (db meter) is an instrument designed to measure the intensity of the waves from a source of sound,

such as a vibrating string, an explosion, etc. Although the units for measuring sound intensity are known as watt/m2, a more practical unit has been developed, the decibel. The relationship between these two units can be evaluated by looking at the decibel levels of a number of familiar noises. The threshold of hearing is defined as the lowest level of sound that the ear can perceive. The threshold of pain is defined as a sound so loud that it can be felt (pain) by the ear in terms of pressure applied to the ear drum.

An age old question asks: If a tree falls in a forest where there is no one to hear it, does it make a sound? To answer this question, the phenomena of sound must be defined. In the physiological sense, there are three requirements for sound:

1. a source of energy, 2. a transmitting medium for the energy, 3. a receiver to receive and decode the energy. In the physical sense, sound is a series of energy disturbances in a material medium, not necessarily requiring a receiver or observer. Therefore, the answer to the above question depends on the definition used.

The formula of speed of sound

VT = 331 m/s + (.6 m/s ^degree C x T) It must be noted this formula works only for sound traveling in air. The temperature must be in units of oC. The unit for the speed of sound is m/s. If the temperature was 19o C then the speed of sound would be: 331 m/s + (.6 m/s ^degreeC x 19o) or 342 m/s