Sound waves

What is sound? Sound is a longitudinal wave, like this compression wave on a Slinky®. The difference: it is AIR that is being compressed.

Why is sound a wave? Sound waves are traveling oscillations of air pressure. Sound waves can interfere. Sound obeys a wavelength and frequency relationship like a wave. Sound doesn’t look like a water wave, or a wave in a stretched string. But it is still a wave.

Loudness and amplitude The loudness of a sound wave depends on its amplitude. Louder sounds waves have larger amplitude pressure variations. A stereo’s speakers move back and forth a greater distance when producing a loud sound than when producing a soft sound.

Pitch and frequency The pitch of a sound depends on the frequency of the sound wave: Low-pitched sounds have lower frequencies. High-pitched sounds have higher frequencies. Humans can hear sound frequencies from about 20 Hz to 20,000 Hz. Following the investigation, students will use the interactive sound wave generator pictured here to test their own hearing range. See slide 25.

Timbre and overtones Most sounds contain multiple frequencies at the same time. Musical instruments produce a fundamental frequency and many overtones (additional frequencies). Overtones give the sound its timbre, its “piano-ness” or “guitar-ness”. Different instruments produce overtones of varying amplitudes for the same note.

Visualizing sound waves Amplitude on the graph below represents pressure, NOT distance!

Frequency Sound has a huge frequency range. Humans can hear sounds in this frequency range: 20 Hz < f < 20,000 Hz. By middle age, most people can only hear sounds less than about 12,000 Hz. Click on this Sound wave generator on page 440 to test your own hearing range.

Audible frequencies Some animals can hear higher and lower frequencies than humans:

Ultrasound technology Medical ultrasound technology uses very high frequency sound waves. Differences in tissue density reflect ultrasound waves back to a detector and allow sophisticated imaging without harm to the patient. Ultrasound is also used in welding, and for non-medical imaging purposes.

Speed Sound waves are fast. The speed of sound in air is 343 m/s (767 mph!) Many military jets are capable of supersonic flights. This (343 m/s) is the speed of sound at room temperature (21° C), at a pressure of one atmosphere. Chuck Yeager was the first person to break the sound barrier. He flew a X-1 rocket plane to a maximum speed of 361 m/s (807 mph).

Speed in various materials Sound travels even faster in water, or ice, or steel. The stiffer the medium, the faster the sound speed tends to be. When sound passes from one medium to another . . . speed and wavelength change frequency stays the same

Speed in various materials A 1000 Hz sound in … AIR has a speed of 343 m/s and a wavelength of 34 cm. WATER has a speed of 1480 m/s and a wavelength of 1.5 m. ICE has a speed of 3500 m/s and a wavelength of 3.5 m.

No sound in a vacuum Sound can’t travel in a vacuum. The loud explosions from space battles in science fiction movies are not realistic. If you were actually watching a space battle from a distant space ship, you would hear total silence.

Amplitude Sound waves have small amplitudes. Typically the variation in pressure is about 0.0001 atmospheres, far below our ability to detect through our sense of touch. BUT our ears are extremely sensitive and can easily detect these tiny pressure oscillations.

Amplitude and loudness The amplitude of a sound wave determines its loudness. Larger amplitude means louder sound. BUT, to a human ear, frequency also matters. A high amplitude sound at a frequency of 40,000 Hz is silent to a human ear but quite loud to a bat!

Loudness and frequency The Equal Loudness Curve shows how sounds of different frequencies compare in perceived loudness to an average human ear. Examine the graph. Which frequencies do we hear the best? Human speech frequencies tend to range between 100 Hz to 2,000 Hz, where our ears are most sensitive. The frequency of a baby’s cry ranges around 3000 Hz (above the range of typical speech) where our ear is very sensitive.

The decibel scale Our ears can detect an enormous range of pressures. For this reason, the logarithmic decibel (dB) scale is used to measure loudness. On the decibel scale, an increase of 20 dB means the wave has 10 times greater amplitude (and 100 times greater power). Power and energy are related to the square of the amplitude of a wave. Point out that most of the sounds and environments we encounter are in the 30 to 100 dB range.

Assessment Based on this graph: What is the frequency of the sound wave? Is this a transverse or longitudinal wave, and why? What can you say about the consistency of the loudness of this sound?

Assessment Based on this graph: What is the frequency of the sound wave? 400 Hz Is this a transverse or longitudinal wave, and why? longitudinal (sound) What can you say about the loudness of this sound? It is constant. Point out that

Assessment Sound waves with a frequency of 172 Hz have a wavelength of 2.0 meters in air. When these waves enter water, their wavelengths change to 8.7 meters. What is the speed of sound in water? A. 19.7 m/s B. 40 m/s C. 1500 m/s D. 2990 m/s

Assessment Sound waves with a frequency of 172 Hz have a wavelength of 2.0 meters in air. When these waves enter water, their wavelengths change to 8.7 meters. What is the speed of sound in water? A. 19.7 m/s B. 40 m/s C. 1500 m/s D. 2990 m/s The frequency stays the same.

The speed of sound and the Doppler effect

Brainstorm Have you ever listened to a siren on an emergency vehicle as it speeds towards you, and then away? The sound of the siren changes pitch as the vehicle passes by. Why? Is it the speed of sound that’s changing?

The speed of sound Sound travels at 343 m/s (767 mph) in air (at 20o C and atmospheric pressure). The speed of sound in air is constant: it doesn’t change, even if the sound source is moving. But the frequency and wavelength of sound do change. Point out – the speed of a wave depends on the medium (air)

Finding the wavelength The siren on a fire engine operates at a frequency of about 2000 Hz. How long are these wavelengths? Asked: λ Given: v Relationships: Solution:

Finding the wavelength The siren on a fire engine operates at a frequency of about 2000 Hz. How long are these wavelengths? Asked: wavelength λ Given: v = 343 m/s, f = 2000 Hz Relationships: Solution:

Finding the wavelength The siren on a fire engine operates at a frequency of about 2000 Hz. How long are these wavelengths? Asked: wavelength λ Given: v = 343 m/s, f = 2000 Hz Relationships: Solution:

Finding the frequency If the siren on a police car has a wavelength of 10 centimeters, what is the frequency of the sound wave? Asked: f Given: λ Relationships: Solution:

Finding the frequency If the siren on a police car has a wavelength of 10 centimeters, what is the frequency of the sound wave? Asked: frequency f Given: v = 343 m/s, wavelength λ = 0.10 m Relationships: Solution:

Finding the frequency If the siren on a police car has a wavelength of 10 centimeters, what is the frequency of the sound wave? Asked: frequency f Given: v = 343 m/s, wavelength λ = 0.10 m Relationships: Solution:

Doppler effect Sheldon dresses as the Doppler Effect… When a siren is at rest, all observers (A, B, C, D) hear the same frequency.

Doppler effect When a siren is at rest, all observers (A, B, C, D) hear the same frequency. But what happens if the source begins to move?

Doppler effect When the siren is at rest, all observers (A, B, C, D) hear the same frequency. What changes as the source begins to move?

Doppler effect Person A hears a higher frequency sound. Person C hears a lower frequency sound.

Why does frequency change? If the speaker moves towards you, the wavefronts bunch up. The wavelength is shorter so the frequency is higher.

Why does frequency change? If the speaker moves away from you, the wavefronts spread out. The wavelength is longer so the frequency is lower.

Calculating the frequency If a source moves with velocity v TOWARDS an observer at rest, the observed frequency is: f  = observed frequency (Hz) f0  = frequency of source (Hz) v  = velocity of the source (m/s) vs  = speed of sound (m/s)

Calculating the frequency A siren with a frequency of 2000 Hz is mounted on a fire engine. If the fire engine heads towards you at 25.0 m/s, what frequency do you hear? Asked: f Given: vs Relationships: Solution:

Calculating the frequency A siren with a frequency of 2000 Hz is mounted on a fire engine. If the fire engine heads towards you at 25.0 m/s, what frequency do you hear? Asked: frequency, f Given: f0 = 2000 Hz, v = 25.0 m/s, vs= 343 m/s Relationships: Solution:

Calculating the frequency A siren with a frequency of 2000 Hz is mounted on a fire engine. If the fire engine heads towards you at 25.0 m/s, what frequency do you hear? Asked: frequency, f Given: f0 = 2000 Hz, v = 25.0 m/s, vs= 343 m/s Relationships: Solution:

Calculating the frequency If the source is moving AWAY from the observer, the same equation applies: BUT the velocity v of the sound source will be a negative number. The resulting frequency will always be lower than f0.

Calculating the frequency A siren with a frequency of 2000 Hz is mounted on a fire engine. If the fire engine is moving AWAY from you at 25.0 m/s, what frequency do you hear? Asked: frequency, f Given: fo = 2000 Hz, v = -25.0 m/s, vs= 343 m/s Relationships: Solution:

Calculating the frequency A siren with a frequency of 2000 Hz is mounted on a fire engine. If the fire engine is moving AWAY from you at 25.0 m/s, what frequency do you hear? Asked: frequency, f Given: fo = 2000 Hz, v = -25.0 m/s, vs= 343 m/s Relationships: Solution:

Supersonic flight Supersonic describes motion at speeds higher than the speed of sound. What happens when a supersonic aircraft moves faster than the sound it makes? What do you hear?

Supersonic flight When an aircraft moves FASTER than the speed of sound, the Doppler equation no longer applies!

Shock waves A shock wave forms at the nose and leading edges of a supersonic aircraft. The shock wave is a result of the constructive interference of the wavefronts.

Shock waves A person standing on the ground will hear a sonic boom as the shock wave passes by. Shock waves can be powerful enough to break windows.

Shock waves The wake of a boat (or even of a duck!) is an everyday example of a shock wave. When an object travels faster than the speed of water waves, a wake is formed by the constructive interference of the waves.

Assessment Calculate the period and frequency of the sound waves depicted in graphs A and B. How do they compare with one another?

Assessment Calculate the period and frequency of the sound waves depicted in graphs A and B. How do they compare with one another? Graph A: T = 0.02 s, f = 50 Hz Graph B: T = 0.04 s, f = 25 Hz. B’s period is twice as long as A’s and B’s frequency is half of A’s.

Assessment An ice cream truck is traveling very fast as it plays its song. As it approaches, the song sounds higher in frequency to the stationary observer. Why is this? The crests of the sound waves are closer together. The truck's speed gives the sound more momentum. The wavelength of the sound increases, increasing the frequency. The ice cream man increases the frequency of his music to get the attention of a potential costumer.

Assessment An ice cream truck is traveling very fast as it plays its song. As it approaches, the song sounds higher in frequency to the stationary observer. Why is this? The crests of the sound waves are closer together. The truck's speed gives the sound more momentum. The wavelength of the sound increases, increasing the frequency. The ice cream man increases the frequency of his music to get the attention of a potential costumer.

Homework Page 465 #1-5, 15, 19, 27, Possible aside: Light waves also show a frequency shift when sources and receivers are moving apart. Stars moving rapidly away from us show a “red shift” in their spectrums. This red shift was the first evidence for the Big Bang.