This is PHYS 1240 - Sound and Music

Lecture 2

Professor Patricia Rankin

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Clickers on

Remember -Learning Team

Graduate student Teaching Assistant

Tyler C Mcmaken

Undergraduate Learning Assistants

Madeline Karr Rishi MayekarMiles Warnke

Professor

Patricia Rankin

Physics 1240 Lecture 2

Today: Waves, Speed of Sound, Simple Harmonic Motion

Next time: SHO – sine function, sine waves

physicscourses.colorado.edu/phys1240

Canvas Site: assignments, administration, grades

Homework – HW1 Due Wed Jan 22nd 5pm

Homelabs – Hlab 1 Due Monday Jan 27th 5pm

Review

Base units:

meters [m] (3.3 ft), kilograms [kg] (2.2 lb), seconds (s)

Prefixes:milli (m) 0.001 1⨯10-3

centi (c) 0.01 1⨯10-2

deci (d) 0.1 1⨯10-1

kilo (k) 1000 1⨯103

mega (M)1,000,000 1⨯106

Problem Solving Tips

1) Draw a picture (if needed!)

2) Write down what you know and what don’t know

3) Write down your solution on paper

4) Use units to check that you did the problem right

Clicker

Pressure is given in units of force per unit area (N/m2).

If you exert a force of 5 mN (millinewtons) on a small area

of 1 mm2, what is the pressure, in SI units?

A) 5⨯106 N/m2

B) 2⨯10-4 N/m2

C) 5⨯103 N/m2

D) 5⨯10-3 N/m2

E) 5 N/m2

𝑃 =𝐹

𝐴

5⨯10−3N

1⨯10−6m2= 5⨯103 ൗN m2

5 mN = 5 10−3 N = 5⨯10−3 N

1 (mm)2 = 1 10−3 m2= 1⨯10−6 m2

Solution

A) 5⨯106 N/m2

B) 2⨯10-4 N/m2

C) 5⨯103 N/m2

D) 5⨯10-3 N/m2

E) 5 N/m2

What is Sound?

Sound is a mechanical disturbance of the pressure in a

medium that travels in the form of a longitudinal wave.

Sound is a mechanical disturbance of the pressure in a

medium that travels in the form of a longitudinal wave.

Unit Symbol Conversion

SI pascal Pa 1 Pa ≡ 1 N/m2

other atmosphere atm 1 atm = 101325 N/m2

otherpounds per

square inchpsi 14.7 psi = 1 atm

Pressure

Force per unit area (e.g. thumbtack, gas molecules hitting

wall, ears, lungs)

Medium

• Sound requires a medium (gas, liquid, or solid) to travel

through (without it, there can’t be pressure disturbances)

• What happens to sound when there is no medium?

• In space no-one can hear you scream….

• Sound speed depends on the phase of the medium (solid,

liquid, or gas)—in what way?

• Faster in solids….easier to transfer disturbance

Compressions &

Rarefactions

Peaks &

Troughs

Longitudinal

Longitudinal: particle displacement is parallel to the

wave’s direction of propagation

Transverse: particle displacement is perpendicular to the

wave’s direction of propagation

A B C D E

Clicker

Which container of gas molecules has the largest

pressure on the bottom surface at the moment shown?

A B C D E

Looking for impacts on

surface….

Clicker

If a person does a cannonball on the edge of a

pond while you are in the middle, will you hear

the sound sooner if you are underwater or above

water?

A. Underwater

B. Above Water

Sound in air travels 343 m/s (767 mph)

Sound in water travels 4.3 times faster than air

Sound in iron travels 14 times faster than air

Medium – liquid faster speed

If a person does a cannonball on the edge of a pond

while you are in the middle, will you hear the sound

sooner if you are underwater or above water?

A) Underwater

B) Above water

Clicker

How fast does the air flow out of your mouth as you sing or

speak?

A) 343 m/s

B) Much faster than 343 m/s

C) Much slower than 343 m/s

D) The air isn’t actually “flowing” out

Speaking/Singing – source of sound……

How fast does the air flow out of your mouth as you sing or

speak?

A) 343 m/s

B) Much faster than 343 m/s

C) Much slower than 343 m/s

D) The air isn’t actually “flowing” out

343 m/s = 770 mph

Category 5 hurricane = 70 m/s = 156 mph

Wave Properties

• Speed (v=343 m/s for air at 20°C and 1 atm)

• Wavelength (λ in meters)

• Frequency (ƒ in hertz)

• 1 Hz = 1 s-1

v = λ ƒ

[m/s] = [m] [Hz]

V comes from velocity…

• Note - graphs of pressure, particle displacement, or particle

velocity look like transverse waves – don’t be fooled!

Start with the simplest

oscillating system

Idealization – ignore mass of spring, air resistance

Pull down on mass and release

Oscillates

(moves up and down in a

regular way)

Period

Amplitude

Amplitude, Period, Frequency

• Amplitude (A in meters): maximum displacement

from equilibrium

• Period (T in seconds): time takes to return to starting

state

• Frequency (f in s-1): number of oscillations a second

• Are the amplitude and period related?

Equilibrium

height

Basic Physics – Two things in

combination

• Elasticity (stiffness): causes system to return

to equilibrium

• Hooke’s law: the farther you extend the

system, the larger the restoring force

• Inertia (mass moving): causes system to

overshoot equilibrium

Equilibrium

height

Key Formula

• frequency ∝stiffness

mass( 𝑓 =

1

2𝜋

𝑠

𝑚)

• Intuitive: trampoline, tight vs. loose string, tuba vs.

flute

Pitch

Only a vibration that repeats itself at regular intervals

produces the sensation of a distinct pitch

pitch – the sensation of how high or low a musical sound

(or note) is

The perceived pitch of a sound is just the ear's response to frequency, i.e., for most practical purposes the pitch is just the frequency.

So – higher frequency, higher pitch

Not all vibrations have a pitch

Vibrations without distinct pitch! The Gong

Relating back to sound:

• Amplitude ↔ loudness

• Frequency ↔ pitch

Period

Amplitude

stiffness = s (N/m)

x

mass = m (kg)

If I increase the amplitude A…

A) the frequency f gets lower

B) the frequency f gets higher

C) the frequency does not change

2-1

Clicker

stiffness = s (N/m)

x

Clicker

mass = m (kg)

If I increase the amplitude A…

A) the frequency f gets lower

B) the frequency f gets higher

C) the frequency does not change

2-1

frequency ∝stiffness

mass

Equilibrium

height

Frequency/Period

• Period (T in seconds): time it takes to return to the

same point of periodic motion

• Frequency (ƒ in hertz): 𝑓=1

𝑇[Hz] =

1

[s]

stiffness = s (N/m)

x

Clicker

mass = m (kg)

If I increase the mass m…

A) the period T gets shorter

B) the period T gets longer

C) The period T depends on how I start the oscillation

2-2

stiffness = s (N/m)

x

Clicker

mass = m (kg)

If I increase the mass m…

A) the period T gets shorter

B) the period T gets longer

C) The period T depends on how I start the oscillation

2-2

frequency ∝stiffness

mass

period ∝mass

stiffness

stiffness = s (N/m)

x

Clicker

mass = m (kg)

If I increase the stiffness s…

A) the period T gets shorter

B) the period T gets longer

C) The period T depends on how I start the oscillation

2-3

stiffness = s (N/m)

x

Clicker

mass = m (kg)

If I increase the stiffness s…

A) the period T gets shorter

B) the period T gets longer

C) The period T depends on how I start the oscillation

2-3

period ∝mass

stiffness

stiffness = s (N/m)

x

Clicker

mass = m (kg)

If I increase the stiffness s…

A) the amplitude A gets smaller

B) the amplitude A gets bigger

C) The amplitude depends on how I start the oscillation

2-4

stiffness = s (N/m)

x

Clicker

mass = m (kg)

If I increase the stiffness s…

A) the amplitude A gets smaller

B) the amplitude A gets bigger

C) The amplitude depends on how I start the oscillation

2-4

Clicker

What is the period (in milliseconds) of a sound wave produced

from a piano playing a middle C (ƒ≈262 Hz)?

A) 262 ms

B) 3.8 ms

C) 3.8⨯10-3 ms

D) 1.3 ms

E) 2.62 ms

What is the period (in milliseconds) of a sound wave produced

from a piano playing a middle C (ƒ≈262 Hz)?

A) 262 ms

B) 3.8 ms

C) 3.8⨯10-3 ms

D) 1.3 ms

E) 2.62 ms

𝑇 =1

𝑓=

1

262 Hz= 0.0038 s

Clicker

Two timpani (labelled A and B) produce sound by a mallet

hitting a vibrating circular membrane. If A has a larger

membrane than B, but A’s membrane is fitted more loosely,

which will have a higher pitch?

A) A

B) B

C) Same pitch

D) Can’t tell without more info

Clicker

Two timpani (labelled A and B) produce sound by a mallet

hitting a vibrating circular membrane. If A has a larger

membrane than B, but A’s membrane is fitted more loosely,

which will have a higher pitch?

A) A

B) B

C) Same pitch

D) Can’t tell without more info