Chapter 16 - Sound Waves Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect Sonic Boom and shock waves

Sound Speed AirSea Water Bulk Modulus 1.4(1.01 x 10 5) Pa 2.28 x 10 9 Pa Density1.21 kg/m kg/m 3 Speed 343 m/s1500 m/s Variation with Temperature: Air Seawater

Pitch is frequency Audible20 Hz – Hz Infrasonic< 20 Hz Ultrasonic>20000 Hz Middle C on the piano has a frequency of 262 Hz. What is the wavelength (in air)? 1.3 m

Intensity of sound Loudness – intensity of the wave. Energy transported by a wave per unit time across a unit area perpendicular to the energy flow. SourceIntensity (W/m 2 )Sound Level Jet Plane Pain Threshold1120 Siren1x Busy Traffic1x Conversation3x Whisper1x Rustle of leaves1x Hearing Threshold1x

Sound Level - Decibel

Stringed instruments

Question 1 A steel wire in a piano has a length of 0.9 m and a mass of 5.4 g. To what tension must this wire be stretched so that its fundamental vibration corresponds to middle C: i.e., the vibration possess a frequency

Wind instruments – Double open ended pipes Frequencies are identical to waves on a string

Wind instruments – Single open ended pipes Only odd harmonics are present

Question 2 – Pepsi Bottle What is the fundamental frequency of a pepsi bottle 32 cm tall when you blow over it. Assume the speed of sound in air is 343 m/s. 5 cm of water are added to the bottle. What is the new resonant frequency. 32 cm

Waves on the surface of a liquid

Two dimensional wave reflection

Interference in Space When the path lengths from source to receiver differ by /2 destructive interference results.

Interference in Time - Beats Two sounds of different frequency: Superposition:

Trig identity again: Interference in Time - Beats Amplitude varies in time at a frequency equal to the difference in the two frequencies Beat Frequency

Beats

Doppler Effect

Doppler Effect – 4 cases Source moving toward receiver Source moving away from receiver Receiver (observer) moving towards source Receiver (observer) moving away from source.

Source moving case Towards: Away:

Receiver (observer) moving case Towards: Away:

Source and receiver moving Numerator – Receiver (observer) –Toward + –Away – Denominator – Source –Toward – –Away +

Doppler Example Intelligence tells you that a particular piece of machinery in the engine room of a Soviet Victor III submarine emits a frequency of 320 Hz. Your sonar operator hears the machinery but reports the frequency is 325 Hz. Assume you have slowed to a negligible speed in order to better hear the Russian. –Is the VIII coming toward you or moving away from you? –Assuming the Victor is either moving directly toward or away from you, what is his speed in m/s?

Shock waves and the sonic boom

Sometimes you hear 2 booms