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Introduction

Now that we have studied the basics of longitudinal waves, we are ready to study sound waves in detail.

Have you ever thought about how amazing your sense of hearing is? It is actually pretty remarkable. There are many types of sounds: a car horn, a laughing baby, a barking dog, and somehow your brain can sort it all out. Though it seems complicated, it is rather simple to understand once you learn a very simple fact. Sound is a wave. So you can use everything you know about waves to explain sound.

Characteristics of a Sound Wave

Since sound is a wave, we can relate the properties of sound to the properties of a wave. The basic properties of sound are: pitch, loudness and tone.

Figure 1: Pitch and loudness of sound. Sound B has a lower pitch (lower frequency) than Sound A and is softer (smaller amplitude) than Sound C.
(a)
Figure 1(a) (PG11C5_001.png)
(b)
Figure 1(b) (PG11C5_002.png)
(c)
Figure 1(c) (PG11C5_003.png)

Pitch

The frequency of a sound wave is what your ear understands as pitch. A higher frequency sound has a higher pitch, and a lower frequency sound has a lower pitch. In Figure 1 sound A has a higher pitch than sound B. For instance, the chirp of a bird would have a high pitch, but the roar of a lion would have a low pitch.

The human ear can detect a wide range of frequencies. Frequencies from 20 to 20 000 Hz are audible to the human ear. Any sound with a frequency below 20 Hz is known as an infrasound and any sound with a frequency above 20 000 Hz is known as an ultrasound.

Table 1 lists the hearing ranges of some common animals compared to humans.

Table 1: Range of frequencies
  lower frequency (Hz) upper frequency (Hz)
Humans 20 20 000
Dogs 50 45 000
Cats 45 85 000
Bats 20 120 000
Dolphins 0,25 200 000
Elephants 5 10 000

Investigation : Range of Wavelengths

Using the information given in Table 1, calculate the lower and upper wavelengths that each species can hear. Assume the speed of sound in air is 344m·s-1344m·s-1.

Loudness

The amplitude of a sound wave determines its loudness or volume. A larger amplitude means a louder sound, and a smaller amplitude means a softer sound. In Figure 1 sound C is louder than sound B. The vibration of a source sets the amplitude of a wave. It transmits energy into the medium through its vibration. More energetic vibration corresponds to larger amplitude. The molecules move back and forth more vigorously.

The loudness of a sound is also determined by the sensitivity of the ear. The human ear is more sensitive to some frequencies than to others. The volume we receive thus depends on both the amplitude of a sound wave and whether its frequency lies in a region where the ear is more or less sensitive.

Tone

Tone is a measure of the quality of the sound wave. For example, the quality of the sound produced in a particular musical instruments depends on which harmonics are superposed and in which proportions. The harmonics are determined by the standing waves that are produced in the instrument. For general interest see Physics of music, which explains the physics of music in greater detail.

The quality (timbre) of the sound heard depends on the pattern of the incoming vibrations, i.e. the shape of the sound wave. The more irregular the vibrations, the more jagged is the shape of the sound wave and the harsher is the sound heard.

Speed of Sound

The speed of sound depends on the medium the sound is travelling in. Sound travels faster in solids than in liquids, and faster in liquids than in gases. This is because the density of solids is higher than that of liquids which means that the particles are closer together. Sound can be transmitted more easily.

The speed of sound also depends on the temperature of the medium. The hotter the medium is, the faster its particles move and therefore the quicker the sound will travel through the medium. When we heat a substance, the particles in that substance have more kinetic energy and vibrate or move faster. Sound can therefore be transmitted more easily and quickly in hotter substances.

Sound waves are pressure waves. The speed of sound will therefore be influenced by the pressure of the medium through which it is travelling. At sea level the air pressure is higher than high up on a mountain. Sound will travel faster at sea level where the air pressure is higher than it would at places high above sea level.

Definition 1: Speed of sound
The speed of sound in air, at sea level, at a temperature of 21C21C and under normal atmospheric conditions, is 344m·s-1344m·s-1.

Sound frequency and amplitude

Study the following diagram representing a musical note. Redraw the diagram for a note

  1. with a higher pitch
  2. that is louder
  3. that is softer
Figure 2
Figure 2 (PG11C5_004.png)
Click here for the solution

Physics of the Ear and Hearing

Figure 3: Diagram of the human ear.
Figure 3 (HumanEar-GrayScale.png)

The human ear is divided into three main sections: the outer, middle, and inner ear. Let's follow the journey of a sound wave from the pinna (outermost part) to the auditory nerve (innermost part) which transmits a signal to the brain. The pinna is the part of the ear we typically think of when we refer to the ear. Its main function is to collect and focus an incident sound wave. The wave then travels through the ear canal until it meets the eardrum. The pressure fluctuations of the sound wave make the eardrum vibrate. The three very small bones of the middle ear, the malleus (hammer), the incus (anvil), and the stapes (stirrup), transmit the signal through to the elliptical window. The elliptical window is the beginning of the inner ear. From the elliptical window the sound waves are transmitted through the liquid in the inner ear and interpreted as sounds by the brain. The inner ear, made of the semicircular canals, the cochlea, and the auditory nerve, is filled with fluid. The fluid allows the body to detect quick movements and maintain balance. The snail-shaped cochlea is covered in nerve cells. There are more than 25 000 hairlike nerve cells. Different nerve cells vibrate with different frequencies. When a nerve cell vibrates, it releases electrical impulses to the auditory nerve. The impulses are sent to the brain through the auditory nerve and understood as sound.

Ultrasound

Ultrasound is sound with a frequency that is higher than 20 kHz. Some animals, such as dogs, dolphins, and bats, have an upper limit that is greater than that of the human ear and can hear ultrasound.

Table 2: Different uses of ultrasound and the frequencies applicable.
Application Lowest Frequency (kHz) Highest Frequency (kHz)
Cleaning (e.g. Jewelery) 20 40
Material testing for flaws 50 500
Welding of plastics 15 40
Tumour ablation 250 2000

The most common use of ultrasound is to create images, and has industrial and medical applications. The use of ultrasound to create images is based on the reflection and transmission of a wave at a boundary. When an ultrasound wave travels inside an object that is made up of different materials such as the human body, each time it encounters a boundary, e.g. between bone and muscle, or muscle and fat, part of the wave is reflected and part of it is transmitted. The reflected rays are detected and used to construct an image of the object.

Ultrasound in medicine can visualise muscle and soft tissue, making them useful for scanning the organs, and is commonly used during pregnancy. Ultrasound is a safe, non-invasive method of looking inside the human body.

Ultrasound sources may be used to generate local heating in biological tissue, with applications in physical therapy and cancer treatment. Focussed ultrasound sources may be used to break up kidney stones.

Ultrasonic cleaners, sometimes called supersonic cleaners, are used at frequencies from 20-40 kHz for jewellery, lenses and other optical parts, watches, dental instruments, surgical instruments and industrial parts. These cleaners consist of containers with a fluid in which the object to be cleaned is placed. Ultrasonic waves are then sent into the fluid. The main mechanism for cleaning action in an ultrasonic cleaner is actually the energy released from the collapse of millions of microscopic bubbles occurring in the liquid of the cleaner.

Note: Interesting Fact :

Ultrasound generator/speaker systems are sold with claims that they frighten away rodents and insects, but there is no scientific evidence that the devices work; controlled tests have shown that rodents quickly learn that the speakers are harmless.

In echo-sounding the reflections from ultrasound pulses that are bounced off objects (for example the bottom of the sea, fish etc.) are picked up. The reflections are timed and since their speed is known, the distance to the object can be found. This information can be built into a picture of the object that reflects the ultrasound pulses.

SONAR

Figure 4
Figure 4 (PG11C5_005.png)

Ships on the ocean make use of the reflecting properties of sound waves to determine the depth of the ocean. A sound wave is transmitted and bounces off the seabed. Because the speed of sound is known and the time lapse between sending and receiving the sound can be measured, the distance from the ship to the bottom of the ocean can be determined, This is called sonar, which stands from Sound Navigation And Ranging.

Echolocation

Animals like dolphins and bats make use of sounds waves to find their way. Just like ships on the ocean, bats use sonar to navigate. Ultrasound waves that are sent out are reflected off the objects around the animal. Bats, or dolphins, then use the reflected sounds to form a “picture” of their surroundings. This is called echolocation.

Exercise 1: SONAR

A ship sends a signal to the bottom of the ocean to determine the depth of the ocean. The speed of sound in sea water is 1450m.s-11450m.s-1. If the signal is received 1,5 seconds later, how deep is the ocean at that point?

Solution
  1. Step 1. Identify what is given and what is being asked: :
    s = 1450 m . s - 1 t = 1 , 5 s there and back t = 0 , 75 s one way D = ? s = 1450 m . s - 1 t = 1 , 5 s there and back t = 0 , 75 s one way D = ?
    (1)
  2. Step 2. Calculate the distance: :
    Distance = speed × time D = s × t = 1450 m . s - 1 × 0 , 75 s = 1087 , 5 m Distance = speed × time D = s × t = 1450 m . s - 1 × 0 , 75 s = 1087 , 5 m
    (2)

Intensity of Sound (Not Included in CAPS - Advanced)

Important: Advanced Section:

This section is more advanced than required and is best revisited for interest only when you are comfortable with concepts like power and logarithms.

Intensity is one indicator of amplitude. Intensity is the energy transmitted over a unit of area each second.

Intensity

Intensity is defined as:

Intensity = energy time × area = power area Intensity = energy time × area = power area
(3)

By the definition of intensity, we can see that the units of intensity are

Joules s · m 2 = Watts m 2 Joules s · m 2 = Watts m 2
(4)

The unit of intensity is the decibel (symbol: dB). This reduces to an SI equivalent of W·m-2W·m-2.

The average threshold of hearing is 10-12W·m-210-12W·m-2. Below this intensity, the sound is too soft for the ear to hear. The threshold of pain is 1.0W·m-21.0W·m-2. Above this intensity a sound is so loud it becomes uncomfortable for the ear.

Notice that there is a factor of 10121012 between the thresholds of hearing and pain. This is one reason we define the decibel (dB) scale.

dB Scale

The intensity in dB of a sound of intensity II, is given by:

β = 10 log I I o I o = 10 - 12 W · m - 2 β = 10 log I I o I o = 10 - 12 W · m - 2
(5)

In this way we can compress the whole hearing intensity scale into a range from 0 dB to 120 dB.

Table 3: Examples of sound intensities.
Source Intensity (dB) Times greater than hearing threshold
     
Rocket Launch 180 10 18 10 18
Jet Plane 140 10 14 10 14
Threshold of Pain 120 10 12 10 12
Rock Band 110 10 11 10 11
Subway Train 90 10 9 10 9
Factory 80 10 8 10 8
City Traffic 70 10 7 10 7
Normal Conversation 60 10 6 10 6
Library 40 10 4 10 4
Whisper 20 10 2 10 2
Threshold of hearing 0 0

Notice that there are sounds which exceed the threshold of pain. Exposure to these sounds can cause immediate damage to hearing. In fact, exposure to sounds from 80 dB and above can damage hearing over time. Measures can be taken to avoid damage, such as wearing earplugs or ear muffs. Limiting exposure time and increasing distance between you and the source are also important steps for protecting your hearing.

Discussion : Importance of Safety Equipment

Working in groups of 5, discuss the importance of safety equipment such as ear protectors for workers in loud environments, e.g. those who use jack hammers or direct aeroplanes to their parking bays. Write up your conclusions in a one page report. Some prior research into the importance of safety equipment might be necessary to complete this group discussion.

Summary

  1. Sound waves are longitudinal waves
  2. The frequency of a sound is an indication of how high or low the pitch of the sound is.
  3. The human ear can hear frequencies from 20 to 20 000 Hz. Infrasound waves have frequencies lower than 20 Hz. Ultrasound waves have frequencies higher than 20 000 Hz.
  4. The amplitude of a sound determines its loudness or volume.
  5. The tone is a measure of the quality of a sound wave.
  6. The speed of sound in air is around 340m·s-1340m·s-1. It is dependent on the temperature, height above sea level and the phase of the medium through which it is travelling.
  7. Sound travels faster when the medium is hot.
  8. Sound travels faster in a solid than a liquid and faster in a liquid than in a gas.
  9. Sound travels faster at sea level where the air pressure is higher.
  10. The intensity of a sound is the energy transmitted over a certain area. Intensity is a measure of frequency.
  11. Ultrasound can be used to form pictures of things we cannot see, like unborn babies or tumors.
  12. Echolocation is used by animals such as dolphins and bats to “see” their surroundings by using ultrasound.
  13. Ships use sonar to determine how deep the ocean is or to locate shoals of fish.

Exercises

  1. Choose a word from column B that best describes the concept in column A.
    Table 4
    Column AColumn B
    pitch of soundamplitude
    loudness of soundfrequency
    quality of soundspeed
     waveform
    Click here for the solution
  2. A tuning fork, a violin string and a loudspeaker are producing sounds. This is because they are all in a state of:
    1. compression
    2. rarefaction
    3. rotation
    4. tension
    5. vibration
    Click here for the solution
  3. What would a drummer do to make the sound of a drum give a note of lower pitch?
    1. hit the drum harder
    2. hit the drum less hard
    3. hit the drum near the edge
    4. loosen the drum skin
    5. tighten the drum skin
    Click here for the solution
  4. What is the approximate range of audible frequencies for a healthy human?
    1. 0.2 Hz 200 Hz
    2. 2 Hz 2 000 Hz
    3. 20 Hz 20 000 Hz
    4. 200 Hz 200 000 Hz
    5. 2 000 Hz 2 000 000 Hz
    Click here for the solution
  5. X and Y are different wave motions. In air, X travels much faster than Y but has a much shorter wavelength. Which types of wave motion could X and Y be?
    Table 5
     XY
    Amicrowavesred light
    Bradioinfra red
    Cred lightsound
    Dsoundultraviolet
    Eultravioletradio
    Click here for the solution
  6. Astronauts are in a spaceship orbiting the moon. They see an explosion on the surface of the moon. Why can they not hear the explosion?
    1. explosions do not occur in space
    2. sound cannot travel through a vacuum
    3. sound is reflected away from the spaceship
    4. sound travels too quickly in space to affect the ear drum
    5. the spaceship would be moving at a supersonic speed
    Click here for the solution
  7. A man stands between two cliffs as shown in the diagram and claps his hands once.
    Figure 5
    Figure 5 (PG11C5_006.png)
    Assuming that the velocity of sound is 330m·s-1330m·s-1, what will be the time interval between the two loudest echoes?
    1. 23s23s
    2. 16s16s
    3. 56s56s
    4. 1 s
    5. 13s13s
    Click here for the solution
  8. A dolphin emits an ultrasonic wave with frequency of 0,15 MHz. The speed of the ultrasonic wave in water is 1 500m·s-11 500m·s-1. What is the wavelength of this wave in water?
    1. 0,1 mm
    2. 1 cm
    3. 10 cm
    4. 10 m
    5. 100 m
    Click here for the solution
  9. The amplitude and frequency of a sound wave are both increased. How are the loudness and pitch of the sound affected?
    Table 6
     loudnesspitch
    Aincreasedraised
    Bincreasedunchanged
    Cincreasedlowered
    Ddecreasedraised
    Edecreasedlowered
    Click here for the solution
  10. A jet fighter travels slower than the speed of sound. Its speed is said to be:
    1. Mach 1
    2. supersonic
    3. subsonic
    4. hypersonic
    5. infrasonic
    Click here for the solution
  11. A sound wave is different from a light wave in that a sound wave is:
    1. produced by a vibrating object and a light wave is not.
    2. not capable of traveling through a vacuum.
    3. not capable of diffracting and a light wave is.
    4. capable of existing with a variety of frequencies and a light wave has a single frequency.
    Click here for the solution
  12. At the same temperature, sound waves have the fastest speed in:
    1. rock
    2. milk
    3. oxygen
    4. sand
    Click here for the solution
  13. Two sound waves are traveling through a container of nitrogen gas. The first wave has a wavelength of 1,5 m, while the second wave has a wavelength of 4,5 m. The velocity of the second wave must be:
    1. 1919 the velocity of the first wave.
    2. 1313 the velocity of the first wave.
    3. the same as the velocity of the first wave.
    4. three times larger than the velocity of the first wave.
    5. nine times larger than the velocity of the first wave.
    Click here for the solution
  14. Sound travels at a speed of 340 m··s-1-1. A straw is 0,25 m long. The standing wave set up in such a straw with one end closed has a wavelength of 1,0 m. The standing wave set up in such a straw with both ends open has a wavelength of 0,50 m.
    1. calculate the frequency of the sound created when you blow across the straw with the bottom end closed.
    2. calculate the frequency of the sound created when you blow across the straw with the bottom end open.
    Click here for the solution
  15. A lightning storm creates both lightning and thunder. You see the lightning almost immediately since light travels at 3×108m·s-13×108m·s-1. After seeing the lightning, you count 5 s and then you hear the thunder. Calculate the distance to the location of the storm.
    Click here for the solution
  16. A person is yelling from a second story window to another person standing at the garden gate, 50 m away. If the speed of sound is 344 m··s-1-1, how long does it take the sound to reach the person standing at the gate?
    Click here for the solution
  17. A piece of equipment has a warning label on it that says, "Caution! This instrument produces 140 decibels." What safety precaution should you take before you turn on the instrument?
    Click here for the solution
  18. What property of sound is a measure of the amount of energy carried by a sound wave?
    Click here for the solution
  19. Person 1 speaks to person 2. Explain how the sound is created by person 1 and how it is possible for person 2 to hear the conversation.
    Click here for the solution
  20. Sound cannot travel in space. Discuss what other modes of communication astronauts can use when they are outside the space shuttle?
    Click here for the solution
  21. An automatic focus camera uses an ultrasonic sound wave to focus on objects. The camera sends out sound waves which are reflected off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 344 m··s-1-1) returns to the camera 0,150 s after leaving the camera, how far away is the object?
    Click here for the solution
  22. Calculate the frequency (in Hz) and wavelength of the annoying sound made by a mosquito when it beats its wings at the average rate of 600 wing beats per second. Assume the speed of the sound waves is 344 m··s-1-1.Click here for the solution
  23. How does halving the frequency of a wave source affect the speed of the waves?
    Click here for the solution
  24. Humans can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 344 m··s-1-1, calculate the wavelength of the sound corresponding to the upper range of audible hearing.
    Click here for the solution
  25. An elephant trumpets at 10 Hz. Assuming the speed of sound in air is 344 m··s-1-1, calculate the wavelength of this infrasonic sound wave made by the elephant.
    Click here for the solution
  26. A ship sends a signal out to determine the depth of the ocean. The signal returns 2,5 seconds later. If sound travels at 1450 m.s-1-1 in sea water, how deep is the ocean at that point?
    Click here for the solution

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