Sound II. of sound waes Standing waes Complex sound waes of sound waes Two sound waes superimposed Constructie Destructie Noise canceling headphones Noise Wae Wae Anti-noise Wae Wae due to path difference r r In phase at x0 path difference δ r r Condition for constructie interference Condition for destructie interference A where m is any integer Superposition of waes at A shows interference due to path differences δ m δ ( m + ) m 0 +, +,. δ0 Constructie δ Destructie Sum
δ Constructie of sound waes Phase shift due to path differences x When r r m Constructie When r r (m+½) Destructie m is any integer An experiment is performed to measure the speed of sound using by separating the sound from a single source along two separate paths with different path lengths and combining them at the detector. For a frequency of.0 khz (assume sound 40 m/s); A) What would the smallest path difference be to obsere a minimum in intensity r r 40 m/ s 5.7x0 m 5.7cm f (x0 s ) B) What would the smallest (non-zero) path difference be to obsere a maximum in intensity. r r cm 4.6 Path difference for two sources. r -r 0. m At position P the listener hears the first minimum in sound intensity. Find the frequency of the oscillation. sound 40 m/s At position P the path difference is equal to /. (first minimum) destructie interference. r r 0.m (0.) 0.6m 40m/ s f.x0 Hz 0.6m Standing Wae Standing Waes Standing waes (waes on a string) Standing waes in air columns. A standing wae is formed by reflections back and forth at the boundaries of a media. The standing wae does not carry energy but seres to store energy. The standing wae stores energy of waes with specific waelengths.
Standing wae on a string Nodes Standing Wae with nodes At different times. The Standing wae doesn t moe it just stands in one place Anti-nodes Fixed end Standing Waes A standing wae is generated by superposition of two waes with the same frequency and waelength traeling in opposite directions. Standing Wae Conditions n One node at each end with additional nodes only at specific positions Distance between nodes / Simulation of a standing wae. http://www.walter-fendt.de/ph4e/stwaerefl.htm n n A string with length can support standing waes of only at certain waelengths. n where n,, integer alues n called the fundamental n called the second harmonic etc. Standing wae frequencies and waelengths Find the fundamental and second harmonics of a steel wire.0m long fixed at both ends. The speed of the wae in the string is 00 m/s n n f f f Generally f f 00 00Hz () f 00 Hz n f f fn n nf where n,,...
Standing waes in air columns Fundamental Frequency ends closed ends open one end open one end closed N N A A N A Cylinder open at both ends Harmonics 4 4 F F F 4 is the speed of sound in air F lower by a factor of f n n f n,,, 4... All harmonics Cylinder open at one end closed at one end - Harmonics Summary For a cylinder with the same length f n nf n,, 5, 7... Only odd harmonics 5f 4f Frequency fn n f 7f f 5f n n fn f f 4 n fn f f n,,... n,, 5... f only odd harmonics all harmonics 0 0 both ends one open open/ closed one closed A cylinder 5.0 cm in length is closed at one end and open at the other end. Find the frequency of the third harmonic of the standing wae in the column. air 40 m/s 4 f 4 String Instruments Musical Instruments 4 f f 4 (40)m / s 5.x0 Hz 4(0.05)m Frequency due to standing waes on the string. The body of the instrument acts as a resonator to moe air to amplify the sound. 4
Musical Instruments Wind instruments The sound is produced by ibrating element (reed, ocal chord) and certain specific frequencies are enhanced by resonance in the air column Complex waes In general sound waes are a combination of different frequencies. The superposition of waes with different frequencies gies rise to the characteristic quality (timbre) of the sound. The different frequencies can be determined by mathematical procedure called a Fourier Transform. Complex waes consist of different frequency components, i.e. harmonics. displacement relatie amplitude Time Frequency 5