Ch 12: Sound Medium vs velocity

• Sound is a compression wave (longitudinal) which needs a medium to compress. A wave has regions of high and low pressure.

• Speed- different for various materials. Depends on the elastic modulus, B and the density, ρ of the material.

v  B/

• Speed varies with temperature by: v  (331 0.60T)m/s  • Here we assume t = 20°C so v=343m/s

 Sound perceptions

• A listener is sensitive to 2 different aspects of sound: Loudness and Pitch. Each is subjective yet measureable.

• Loudness is related to Energy of the wave

• Pitch (highness or lowness of sound) is determined by the frequency of the wave.

• The Audible Range of human hearing is from 20Hz to 20,000Hz with higher frequencies disappearing as we age. Beyond hearing

• Sound frequencies above the audible range are called ultrasonic (above 20,000 Hz). Dogs can detect sounds as high as 50,000 Hz and bats as high as 100,000 Hz. Many medicinal applications use ultrasonic sounds.

• Sound frequencies below 20 Hz are called infrasonic. Sources include earthquakes, thunder, volcanoes, & waves made by heavy machinery. Graphical analysis of sound • We can look at a compression (pressure) wave from a perspective of displacement or of pressure variations. The waves produced by each are ¼ λ out of phase with each other. Sound Intensity

• Loudness is a sensation measuring the intensity of a wave.

• Intensity = energy transported per unit time across a unit area. I≈A2

• Intensity (I) has units power/area = watt/m2

• Human ear can detect I from 10-12 w/m2 to 1w/m2 which is a wide range!

• To make a sound twice as loud requires 10x the intensity.

• In the open sound intensity follows inverse square law as you get farther from the source.

Decibels, dB

• We measure sound intensity levels, β using a logarithmic scale having a unit of bels. • 1 decibel, dB is 0.1 bel (10dB =1bel)

-12 2 • I0 is the minimum intensity audible (1x10 W/m ) and the log is base 10, so we define intensity level as

I  10log

I0 • The threshold of hearing would be 0dB • Each 10dB increase is 10x the intensity. (20dB = 100x intensity of 0dB; 30dB = 1000x >0dB) Vibrating Strings • Recall how standing waves are made on a string…

• Fundamental- pitch determined by lowest resonant frequency where nodes are only at the ends. Here λ=2L so v=f/2L on the string.

• Strings on some instruments are the same length, but sound different b/c each has a different m/L which effects velocity:

v  FT /(m/L) • Adjusting tension is how we tune the instrument

• Velocity on a heavy string is less and f will be less for the same λ.  Ex 12-6 Piano strings

• The highest key on a piano corresponds to a frequency about 150 times that of the lowest key. If the string of the highest note is 5.0cm long, how long would the string for the lowest note be if it had the same mass per length and was under the same tension?

• Solution: The velocity would be the same on each string so the frequency is inversely proportional to the length L of the string (f=v/λ= v/2L) Solution cont’d

L f • Thus L  H where the subscripts L and H refer to low L H f L and high notes. It follows that

LL  LH ( f H / fL )  (5.0cm)(150)  750cm  7.5m • This would be too long for a piano so the longer lower strings are made heavier to avoid this.  Amplification

• Stringed instruments need a ‘sounding board’ to help amplify the sound by putting a greater surface area in contact with the air. This produces a stronger wave.

• Other instruments use a column of air to set up a standing wave.

• The fundamental frequency on a string has antinodes at both ends and a single anti node. Harmonics or overtones are whole # multiples of the fundamental.

pipes

• In a pipe the air is vibrating forming the standing wave

• We can discuss the waves by the air displacement OR by the pressure in the air. (Recall these are separated by ¼ a λ)

• We can have pipes that are open at both ends (called open tubes) or that are closed at one end (closed tube).

• Read last paragraph on pg 358- first 2 on page 359 about air displacement on open tubes like a flute.

Pipe diagrams Ex 12-8 open & closed organ pipes

• What will be the fundamental frequency and first three overtones for a 26cm long organ pipe at 20°C if it is (a) open and (b) closed?

• Solution: At 20°C, the speed of sound in air is 343m/s. • (a) For an open pipe, the fundamental frequency is v 343m /s f    660Hz 1 2L 2(0.26m) • The next 3 overtones would be 1320 Hz, 1980 Hz, 2640 Hz and so on…

• (b) For a closed pipe, the fundamental is v 343m /s f    330Hz 1 4L 4(0.26m) • The next 3 overtones will only be heard at odd multiples so we have 990Hz, 1650 Hz, and 2310 Hz  Interference- beats

• As two or more waves superimpose, their amplitudes add algebraically.

• We have constructive interference when waves are in phase and destructive when out of phase.

• Beats occur when sound waves have frequencies close but different. As the waves interact a listener perceives sound levels that alternately rise and fall.

• Beat frequency is found as the difference between the 2 waves.

• A 400 Hz tone and a 396 Hz tone will have a fbeat=4Hz Doppler effect

• Recall wave speed depends only on medium.

• If a source or listener move relative to a wave, the wave frequency (and therefore wavelength) can be perceived to change resulting in a change in pitch. Perceived frequency

• The shift in wavelength is directly proportional to the speed of the source, vs. • The new frequency, f ’ will then be: f f   v  •  1  s  for a source moving toward you •  v  this is called blue shift f f   v  •  1  s  for a source moving away (red shift)  v 

 Doppler effect in space Your turn to prac

• Please do Ch 12 Review pgs 375-378

• Problems # 4, 29, 36, 48, 55

• 1998 FRQ B5