Wave phenomena

Physics 12Source: Giancoli Chapters 11 and 12

Sound waves

How are sound waves produced? Is sound a transverse or longitudinal

wave?

Sound waves

Sound is caused by the vibration of an object which causes air pressure variations.

The frequency range detectable by the normal human ear is 20 Hz – 20,000 Hz

Sound wavesSound wave in a tube (simulation)

What factors might affect the speed of sound?

Sound waves

The speed of sound is given by the expression:

v = √(B/ρ)where B is the bulk modulus (how compressible

the medium is)

and ρ is the density of the medium

Sound waves

If a medium has a LOW bulk modulus, B, that means EASILY compressed.

If a medium has a HIGH bulk modulus it is DIFFICULT TO compress.

Order gases, liquids, and solids in order of increasing bulk modulus.

Which one transmits sound more quickly?

Sound waves

If sound is traveling through air, what variables might affect the speed of sound?

Sound waves

The speed of sound at room temperature (20C) and normal atmospheric pressure is 343 m/s.

How might increased temperature and pressure affect the speed of sound?

Sound waves

A sound wave with a frequency of 300 Hz travels through the air.

(a) What is its wavelength?

(b) If its frequency is increased to 600 Hz, what is its wave speed and the wavelength?

Sound waves

(a) λ = 1.14 m

(b) v = 343 m/s; λ = 0.57 m

Sound waves

Sound waves transmit energy. The rate at which they transmit energy

per unit area is called intensity. Intensity is responsible for a sound’s

loudness level.

Beats

When two sound waves that are similar in frequency interfere, a beat frequency is produced.

A beat is perceived as a modulation in amplitude (loud then soft then loud then soft).

The beat has its own frequency, measured by:

fbeat = | f1 – f2 |

Beats

A piano tuner uses a tuning fork to adjust the key that plays the A note above middle C ( which is 440 Hz). The tuning fork emits a perfect 440 Hz tone. When the tuning fork and the piano key are struck, beats of a frequency of 3 Hz are heard.

(a) What is the frequency of the piano key?

(b) If the piano’s key frequency is too high, should the piano tuner tighten or loosen the string?

Beats

(a) either 437 Hz or 443 Hz

(b) loosen

Resonance

Standing waves can also occur for sound waves.

There are two typical situations: Closed tube (closed at one end) Open tube (open at both ends)

http://www.physics.smu.edu/~olness/www/03fall1320/applet/pipe-waves.html

Resonance

Resonance

A closed-end tube resonates at a fundamental frequency of 440.0 Hz. The air in the tube is at a temperature of 20C, and it conducts sound at a speed of 343 m/s.

(a) What is the length of the tube?

(b) What is the next higher harmonic frequency?

(c) Answer the questions assuming that the tube were open at both ends.

Doppler effect

When a source of sound and the observer are stationary, does the frequency of the sound change?

What will happen if the source or the observer moves?

Ripple tank simulation

Doppler effect

The shift in frequency and wavelength that occurs when the source and detector are in relative motion is called the Doppler effect.

Relative motion Effect on frequency

towards each other

away from each other

Doppler effect

The frequency perceived by the observer is expressed as follows:

where f ‘ is the frequency perceived

f is the frequency at which sound is emitted

v is the speed of sound

vO is the speed of the observer

vS is the speed of the source

Doppler effect

If the detector is moving towards the source, you expect an upward shift in frequency therefore you use addition.

If the source is moving towards the detector you expect an upward shift therefore you use subtraction (smaller denominator).

Doppler effect

A source of 4 kHz sound waves travels at 1/9 the speed of sound towards a detector that’s moving at 1/9 the speed of sound toward the source.

(a) What is the frequency of the waves as they’re received by the detector?

(b) How does the wavelength of the detected waves compare to the wavelength of the emitted waves?

Doppler effect

(a) 5 kHz

(b) shorter