Physics - Vibrations & Sound

Fundamental frequency of a stretched string/wire

f = √(T/µ)/2l

Harmonics that may be present in a pipe closed at one end

Odd harmonics; f = c/4l

Sound wave phenomena examples

-A sensor can be used to pick up the frequency of machines that produce a constant noise in industry and the same sound wave produced out of phase with the source, causing destrucitve interference to occur and reducing the intensity of the noise pollution -Music played in concert halls sounds pleasing due to strategic reflection of sound in the architecture

Experiment to measure speed of sound in air precautions

-As identifying the point where sound is loudest is difficult, repeat this measure several times and find the average length -Avoid parallax error when using meterstick

Experiment to investigate variation of stretched string's fundamental frequency with tension precautions

-Keep length constant -Ensure paper rider is at centerpoint of string as this is the location of the antinode -Avoid parallax error when using meterstick

Experiment to investigate variation of stretched string's fundamental frequency with length precautions

-Keep tension constant -Ensure paper rider is at centerpoint of string as this is the location of the antinode -Avoid parallax error when using meterstick

Resonance examples

-Singer shattering a crystal wine glass with high-pitched note, Tacoma Bridge collapse, soldiers having to march out of step when walking over a bridge to avoid resonance

Experiment to measure speed of sound in air

1. Measure internal diameter of resonance tube using Vernier calipers. 2. Almost submerge resonance tube in graduated cylinder of water. 3. Strike tuning fork and position above pipe. 4. Raise pipe until resonance occurs and measure distance between top of tube and surface of water using meterstick. 5. Repeat using 6-7 tuning forks of different frequencies. 6. Calculate speed of sound in air using c = 4f(l + 0.3d)

Experiment to investigate variation of stretched string's fundamental frequency with length

1. Place paper rider in center of string stretched by tension control key near fixed bridge on one end and newtonmeter near movable bridge on other, all on sonometer. 2. Strike tuning fork and position it on fixed bridge. 3. Slide movable bridge away from fixed bridge until paper rider jumps off rider due to resonance occurring in the wire and measure distance between bridges using meterstick. 4. Repeat using 6-7 tuning forks of different frequencies. 5. Graph frequency against reciprocal of length; they are directly proportional.

Experiment to investigate variation of stretched string's fundamental frequency with tension

1. Place paper rider in center of string stretched by tension control key near fixed bridge on one end and newtonmeter near movable bridge on other, all on sonometer. 2. Strike tuning fork and position it on fixed bridge. 3. Vary tension of wire by adjusting tension control key until paper rider jumps off rider due to resonance occurring in the wire and measure distance between bridges using meterstick. 4. Repeat using 6-7 tuning forks of different frequencies. 5. Graph frequency against square root of tension; they are directly proportional.

Harmonics that may be present in a pipe open at both ends

All harmonics; f = c/2l

Harmonics that may be present in a stretched string

All harmonics; f = c/2l

Experiment to demonstrate interference of sound waves or show sound is a wave motion

Connect two speakers set to the same frequency to a signal generator and walk in a straight line in front of them; differences in intensity of sound due to interference can be observed

Reflection of sound waves

Echos

Sound

Form of energy that travels by longitudinal mechanical waves

Harmonic notation

Frequency of 1st harmonic = f Frequency of 2nd harmonic/1st overtone = 2f Frequency of 3rd harmonic/2nd overtone = 3f etc.

Doubling sound intensity

Increases sound intensity level by 3dB

Why does sound tend to travel faster in denser media?

It is easier and faster to pass a disturbance from one particle to another in denser media

Factors the fundamental frequency of a stretched string/wire depends on

Length l, tension T, mass per unit length µ

Fundamental frequency (f or f₀)

Lowest natural frequency of vibrating object; natural frequency of sound-producing vibrating object; first harmonic; f = c/2l or f = c/4l

Harmonics/overtones

Multiples of the fundamental frequency

Antinode

Point on stationary wave with maximum vibration

Node

Point on stationary wave with no vibration

Experiment to show sound needs a medium to travel through

Ring battery-powered bell, place in sealed bell jar and evacuate air from jar using vacuum pump; as the air is evacuated the volume decreases; when there is no air no sound can be heard.

Applications of threshold of hearing

Ringtones only young people can hear, high-pitched noises emitted outside supermarkets to discourage young people from loitering, dog whistles

Sound intensity level

Scale that compares a particular osund intensity to the threshold of hearing; scalar quantity measured in decibels

Experiment to show resonance

Set up Barton's pendulum (several pendulums of varying length hanging from horizontal string, two being the same length) and set pendulum with same length as other oscillating; pendulum of same length oscillates with a large amplitude because it shares a natural frequency with the one set oscillating, causing resonance to occur

Quality of note

Shape of sound wave, depending on number and amplitude of harmonics present

Decibel adapted scale

Sound intensity level scale adapted for the ear's frequency response, measured with sound level meter

Refraction of sound waves

Sound travels at different speed in different media and temperatures. It travels faster in warm media, making it possible to hear noises from greater distances at night

Natural frequency

The frequency a body oscillates at when vibrating freely

Amplitude of sound wave

The greater the amplitude the louder the sound

Frequency of sound wave

The higher the frequency the higher the pitch

Resonance

The rapid amplification of oscillation when a periodic force is applied at the same frequency as a body's natural frequency

Sound intensity (I)

The rate at which sound energy passes a unit of area perpendicular to the wave's propogation's direction; scalar quantity measured in watts per meter squared (Wm⁻²); I = P/A

Threshold of hearing (I₀)

The smallest sound intensity detectable by the average human ear at a frequency of 1 kHz; 1x10⁻¹² Wm⁻²

Why can't sound waves be polarized?

They are longitudinal, not transverse

Stationary/standing wave

Wave that remains in a constant postion made of series of nodes/antinodes

When are stationary waves produced?

When two periodic traveling waves of the same frequency and amplitude moving in opposite directions combine, or by a periodic traveling wave being reflected upon itself

Derivation of f = c/2l and f = c/4l

c = fλ c = f(2l) or c = f(4l) (because the wavelength is twice or four times the length of a string) f = c/2l or f = c/4l

Internode/interantinode distance

λ/₂