Sound

Objectives Understand the properties of sound waves. Understand the concepts of pitch and loudness. Know what factors affect the speed of sound.

Sound Waves Vibrating objects produce longitudinal sound waves. Applet tuning fork demo compression: high pressure rarefaction: low

Human Hearing Human hearing range is 20 – 20000 hz. infrasonic < 20 hz ultrasonic > 20000 hz pitch = frequency (rate of vibrations) loudness: related to amplitude

Speed of Sound Sound travels through different media at different speeds (but not through a vacuum). Speed depends on… density (solid > liquids > gases) temperature (T↑, v↑) v = 331.5 + 0.607·T (in m/s, T in Celsius) elasticity (tendency to return to original shape)

A jet makes a high pressure ridge as it passes the speed of sound. This high pressure can cause water vapor to condense, forming a cloud.

Intensity and Loudness Loudness is the human perception of sound intensity. Sound intensity is related to the power. intensity = power passing through area (W/m2) What is the intensity of a 15-W speaker at 2.5 m? r power (W)

Decibel Scale decibels (dB): a relative measure of sound intensity; uses a logarithmic scale # of dB : 0 – 10 – 20 – 30 – 40 – etc. intensity: 10X 10X 10X 10X loudness: 2-3X 2-3X 2-3X 2-3X quiet whisper ≈ 20 dB vacuum cleaner ≈ 70 dB lawn mower ≈ 90 dB threshold of pain ≈ 120 dB jet engine ≈ 150 dB

Decibel Calculations Io is threshold of human hearing = 1x10-12 W/m2     Io is threshold of human hearing = 1x10-12 W/m2 How many decibels is a 0.0028 W/m2 sound? What is the intensity (in W/m2) of a 62 dB sound?

Resonance natural frequency: the frequency at which an object naturally vibrates (large = low, small = high) forced vibration: a periodic applied force that causes something else to vibrate example: swingset resonance: an increase in vibrational amplitude; occurs if forced vibration frequency = natural frequency examples: resonators, sound boxes, crystal glass, microwave ovens, Tacoma Narrows bridge, sunscreen

Harmonics fundamental frequency (f1) = longest wavelength standing wave that forms (1 antinode) harmonic frequencies (f2, f3, etc.) are shorter, whole number multiples of the fundamental frequency (2A, 3A, etc.) These harmonics combine into a single waveform.

Harmonics in a String Standing waves occur in stringed instruments. f1: L = 1/2 · l Harmonics f2: L = 2/2 · l fundamental frequency (f1) 2nd harmonic (f2) 3rd harmonic (f3) 4th harmonic (f4), etc. f3: L = 3/2 · l fn: L = n/2 · l

Stringed Instrument Problem A banjo string has mass-to-length ratio of 5.8 x 10-3 kg/m. What will be the 3rd harmonic frequency if the string is 65 cm long and it has a tension of 78 N?

Harmonics in Tube open-end tube n = 1, 2, 3, 4… Who is this? Tube Harmonics open-end tube n = 1, 2, 3, 4… Who is this? closed-end tube n = 1, 3, 5, 7…

Objectives Understand the concept of the Doppler effect and how it causes the formation of bow waves and shock waves. Understand the concept of beats. Understand the concept of timbre.

Doppler Effect Doppler effect: a change in perceived wave frequency caused by relative motion see it approaching: freq ↑ receding: freq ↓ If source speed > wave speed bow wave: 2-D (V-shape) shock wave: 3-D (cone-shape)

Beats beats: a frequency caused by interference of two waves of different frequency Beat Frequency fb = |f1 – f2| Beats caused by interference between transmitted microwaves and Doppler shifted microwaves cause beats—your speed is then calculated by the “radar gun.”

Timbre timbre (tam-ber or tim-ber): the unique quality of sound produced by a musical instrument caused by multiple harmonics The same note is played, but the clarinet has more harmonic frequencies.