SPH3U: Waves & Sound

Wave Speed & Sound

The Universal Wave Equation

Recall that the frequency of a wave is the number of complete cycles that pass a given point in the medium per a unit of time.

Frequency is important for us, because it is the frequency of a sound wave that will determine what pitch (musical note) is being heard.

The Universal Wave Equation

The frequency of the wave is the same as the frequency of the source. It is the source alone that determines the frequency of the wave. Once the wave is produced, the frequency never changes, even if its speed and wavelength do. Likewise the period of the wave can never change, because it is the inverse of the frequency.

The Universal Wave Equation

Speed is defined as the time it takes to go a certain distance.

For a wave, we consider the speed of the wave to be the distance traveled by the wave during one cycle or period of the source.

The Universal Wave Equation

Waves travel one wavelength in the time required for one complete vibration of the source.

So we end up with:

this can also be written as

periodwavelength

Tv

The Universal Wave Equation

this can also be written as

))(( wavelengthfrequencyfv

Factors that Affect Wave Speed

Temperature: Warmer gases transmit waves faster

Properties of the material In a string - Linear Density & Tension is

a factor. Very tight strings transmit energy more effectively. Less dense strings also transmit wave energy more effectively.

Speed of Wave on a String

The equation for the speed of a wave along a string is:

where v is the speed in m/s, Ft is the force of tension, and μ is the linear density.

TFv

Speed of Wave on a String

The linear density, or mass per unit distance, determines how much force it will take to make the string vibrate. Linear density μ, can be calculated using the formula:

where μ is the linear density, m is the mass (kg), and L is the length (m).

Lm

Producing (Making) Sound

Sound Energy that travels as longitudinal waves. Some parts have high pressure and some parts have low pressure.

** The source of every sound is a vibrating object.

Producing (Making) Sound

http://phet.colorado.edu/en/simulation/sound

http://www.physicsclassroom.com/class/sound/u11l1c.cfm

Producing (Making) Sound

Sound Vibrating Object

Human Voice Vocal Chord vibrates

Guitar Strings on Guitar vibrate

Producing (Making) Sound

Sound waves need to travel through a medium like air. Therefore, there is no sound in space!

http://www.youtube.com/watch?v=ce7AMJdq0Gw

The Speed of Sound

Remember that sound travels by making air molecules move. This means that the speed of sound is limited by how fast the molecules can move, which is related to the temperature and density of the medium. If we increase the temperature of the molecules, the speed of sound should increase also.

The Speed of Sound

When the temperature is 0ºC and the atmospheric pressure is 101 kPa, the speed of sound in air is 331m/s. The speed of sound in air increases by 0.59m/s for each rise of 1ºC in temperature.

The Speed of Sound

Equation for speed of sound in air

T

Csm

sm

v

)59.0(331

Example Problem 1

Calculate the speed of sound in air when the temperature is 16°C.

Example Problem 1

Calculate the speed of sound in air when the temperature is 16°C.

Example Problem 1

Speed of Sound

The speed of sound is also effected by the medium. Sound travels most rapidly in certain solids, less rapidly in many liquids, and quite slowly in most gases.

Table 1 – pg. 395 lists the speed of sound in different materials.

MACH Number

Sometimes we describe how fast something is travelling by comparing it to the speed of sound. The ratio of the airspeed of an object to the local speed of sound is called a Mach number.

Mach Number = airspeed of object / local speed of sound

MACH Number

When an object is travelling at Mach 1, it is travelling at the same speed as sound.

When an object is travelling at Mach 2, it is travelling at twice the speed of sound.

Hearing Sound

The audible region of the sound spectrum for humans – The part that we can hear – is from 20 Hz to 20kHz. (Recall: Hz means “1/second”).

Hearing Sound

Frequencies lower than 16 Hz are called Infrasonic.

Frequencies higher than 20 000 Hz are called ultrasonic.

Ultrasound waves have many uses make images of inside of the body

Loudness

Loudness describes how humans perceive sound energy. The loudness of a sound wave is based on its amplitude. The larger the amplitude of the wave, the louder the sound will be. The amplitude of a wave is an indication of how much energy is being transferred.

Loudness

The amount of sound energy being transferred per unit area is called sound intensity.

Intensity the amount of sound energy passing each second through a unit area.

Intensity

Sound intensity is most commonly measured in Bells or Decibels. 1 Decibel (dB) = 10-12 Watts / meter2.

For humans the threshold of hearing is 0 dB and the threshold of pain is 130 dB.

The intensity of sound decreases as the distance from the source increases.

Homework

Read through Sections 8.4-8.5. Make your own notes of things that are of interest. Add them to the notes you have taken in class.

Complete the following questions for homework: Section 8.4 page 391 # 1-6 Section 8.5 page 397 # 2-6

** Make note of questions you didn’t understand – put them on our classroom blackboard!