Quarkphysics.ca



Updated: Aug 2006

Course: sph 3U1

Unit: sound

Lesson 6: Title: Speed of sound

Apparatus needed:

Preliminaries:

Lesson:

Speed of Sound

The speed of sound in air depends on a number of things: (ask class)

air pressure, altitude (density), air composition (humidity), temperature. (Ask how each one could affect the speed of sound). The temperature dependence of the speed of sound is the most noticeable.

empirical formula: v = 331 m/s + 0.6T ; where T is the temperature in (C.

Example: What is the speed of sound at room temperature? in km/hr?

The frequency of a wave is determined by the frequency of the source, therefore the frequency

is generally known or at least unchanged by the medium through which it is travelling.

The velocity of a sound wave travelling through air does not vary with the air pressure, but it

does depend on the temperature of the air. The pressure of the air is caused by the velocity of

the air molecules. The square of this velocity is proportional to the temperature in kelvins (i.e. in

degrees measured with respect to absolute zero (0 deg.K = -273 deg.C) :

The velocity of a sound wave is thus proportional to the velocity of the molecules of the air

through which the wave travels. Thus the velocity of a sound wave at a temperature T is

If v=344 m/s at 20 deg.C, then at temperature Tdeg. kelvin

Source:

Sound (or any vibrations) travel faster in more rigid materials. i.e. solids, then liquids, then gases. In a later lab we will measure the speed of sound.

If you put your head on a railway track (don’t do it!) you would hear the train with the ear on the iron before you heard it with your ear through the air. [Actually, this would work better if there were a sudden noise, like a hammer hitting the track. Another variable is how much the sound is dampened (dissipates) in each medium – I think it would travel farther in steel.]

How far away would something have to be for you to hear a difference between the two media?

(i) p 255 – find the time interval required for us to hear two distinct sounds (i.e. like an echo) [t >0.1s].

(ii) speed of sound in air (at room temperature) =

(iii) speed of sound in steel/iron at room temperature =

(iv) formula: (t = tair – tsteel

= dair/vair – dsteel/vsteel Now fill in all the numbers, note that the two distances are the same, and solve for d. (I think around-about d >= 37 m)

Sound Barrier

What is the sound barrier? In the past, it was thought of as something like the 4 minute mile ( theoretically possible, but physically impossible.

What happens when something goes faster than the speed of sound? - pressure waves build up.

(draw diagram, see p 356) -- sonic boom (refer to Innu in Labrador)

Planes - 50 years ago Chuck Yeager - first man to go faster than the speed of sound in rocket powered Bell X-1.

Typically planes would experience huge vibrations and loss of control as they got close to the speed of sound. Most planes crashed. Sometimes the wings would fall off. Many test pilots were killed. It turns out that the wings go supersonic first because the air is fastest over the tops of the wings. The shock wave destroys the laminar flow over the wings (and control surfaces) and destroys lift. Need wings that are swept back (delta shape), thinner, and enough speed to go faster than the speed of sound (no good just sitting at 340 m/s.

If you are sitting in the front of the plane, it is impossible to hear any sound from the engines as they are behind you and you are moving faster than the sound can get to you (through the air). (Of course, you still feel the vibrations transmitted through the fuselage.)

Name some supersonic planes: (Concorde: white elephant $$; space shuttle -- no)

Mach Number

When the speed of an object is more than the speed of sound (at whatever the local temperature is) we often refer to the speed as a multiple of the speed of sound. example: Mach 2 = 2 x sound

Mach # = vobj / vsound

example: What is the mach number of a jet that is going at 2500 km/hr where the speed of sound is 300 m/s?

Doppler Effect:

This doesn’t really fit anywhere. - how does it tie in? (maybe after beat frequency?)

What happens when the sound source is moving? What do you hear when a car comes towards you and goes past? When a sound source is moving towards you, the waves bunch up so the frequency that you hear is higher. Similarly, the waves behind the car are spaced out further, making a lower frequency & pitch. This effect is called the doppler effect.

Show diagram in “Sound and Hearing”.

DEMO: pretend to throw a tuning fork towards the class. Get some thing that makes a constant noise and swing it on a string.

Of course, there is a formula to describe it ...

[pic] where: f=true freq, f’ = doppler freq, vs = speed of sound

vobj = speed of object (source) -/+ = towards/away

Example: A car horn sounding at 4000Hz is approaching at 20 m/s. What frequency do you hear?

Applications: (explain how each works – with a diagram)

Doppler radar -- police radar to determine speed of cars,

speed of planes (airport radar),

doppler radar for weather? (simple radar – finds location of rain (or planes) – doppler used to determine wind gusts (if there is rain)

light has the same effect: if a light source is moving away from us it looks redded, towards us looks bluer. This is really only seen in stars & galaxies – also used in laser doppler speed detectors by police.)

In every direction we look, the light from stars is redder than it should be. – they are all moving away from us. The normal conclusion is that the universe is expanding, but maybe we just smell bad.

Homework: p241#1,3; p246#1,2,3,6; p269#1; 270 #3,4 (or p272#3,4)

Evaluation: many students are interested in more about sonic booms -- mention that the crack of a whip/towel/flag is due to the end breaking the sound barrier. (is this an urban legend?)

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