RESONANCE & SOUND Amplification

A IR C OLUMN  When a wave source is held at the open end of a pipe, it sends down a wave that reflects from the closed end of the pipe.  If the length of the pipe is just right, the reflected wave can combine with the incident wave to establish a standing wave pattern.  The sound you hear depends on the length of the air column in the pipe relative to the length of the standing wave.

A IR C OLUMN  If an antinode occurs at the open end of the pipe a point of resonance (resulting from constructive interference) occurs at the open end of the pipe and the sound appears to be amplified.  However, if the open end of the pipe does not coincide with the position of an antinode, then little sound can be heard because the incident wave

A IR C OLUMN

N ODES & A NTINODES  Nodes are located every half-wavelength from the end at which the wave is reflected  Antinodes in the air column are located one quarter- wavelength from the end of the pipe where reflection occurs, and then every half-wavelength from that point

A IR C OLUMN A tuning fork with a frequency of 384 Hz is held above an air column. As the column is lengthened, a closed-pipe resonant point is found when the length of the air column is 67.5 cm. What are possible wavelengths for this data? If the speed of sound is known to be slightly greater than 300 m/s, what is the actual wavelength, and the actual speed of sound?

A IR C OLUMN A tuning fork with a frequency of 256 Hz is held over a closed air column. The temperature of the air is 19  C. Find the shortest length of the column that will produce resonance.

S TRING I NSTRUMENTS  A string of a musical instrument is simply a tightly stretched spring for which the simplest standing wave possible is a single antinode with a node at either end.  The fundamental frequency is the lowest frequency produced by a particular instrument.

S TRING I NSTRUMENTS  The frequencies above the fundamental frequency that may exist simultaneously with the fundamental frequency are called overtones.

S TRING I NSTRUMENTS 1. A string of length m is stretched tightly between two fixed ends. The string is plucked and a vibration is created that travels with a speed of 125 m/s along the string. a) Sketch the fundamental wave and first two overtones produced in the string. b) Use your sketches to determine the fundamental frequency and frequencies of the overtones. c) Are the overtones harmonics of the fundamental frequency?

W IND I NSTRUMENT  Wind instruments produce different musical notes by changing the lengths of air columns  The distance from one antinode to the next is one-half a wavelength. Thus, the longest wavelength that can resonate in an open pipe is twice as long as the pipe.

W IND I NSTRUMENT

 In a clarinet or oboe, for example, the effective length of the pipe is changed by covering or uncovering holes at various lengths down the side of the pipe.  The strongest or most resonant frequency will be the wave whose length is twice the distance from the mouthpiece to the first open hole.

W IND I NSTRUMENT Use 344 m/s as the speed of sound in this case. a) Sketch the fundamental wave and the first two overtones for a vibrating closed-end air column produced in a tube that is m long. b) Find the wavelengths and frequencies for these resonances. c) Are the overtones harmonics?

W IND I NSTRUMENT  Determine the length of an open-end air column required to produce a fundamental frequency (1st harmonic) of 480 Hz.

S PEED OF S OUND

If an object is 6.56 m from the camera and sound travels at 344 m/s, determine the length of time it takes the emitted sound pulse to return to the camera.

S PEED OF S OUND

 What is the wavelength of a sound of frequency 225 Hz that is produced in air at a temperature of 20.0°C?

I NTENSITY  Our ears are marvellous organs.  They can respond to the faintest of whispers or the roar of a jet engine.  The ability to distinguish variations in loudness is an important environmental cue that humans and other animals use to navigate in their surroundings.

I NTENSITY  The intensity of a sound is the energy per unit area that passes a point each second.  It has units of (J/m 2 )/s or J/s·m 2,  which is the same as W/m 2.  Our ears can respond to sounds as faint as one-trillionth of a watt per square metre

D ECIBEL S CALE

 The Greek letter beta, , is commonly used to represent sound intensity expressed in dB.  The faintest sound that humans can hear represents the start of the decibel scale and is given a value of 0 dB.  The decibel scale is a logarithmic scale that corresponds to how our ears perceive loudness.

D ECIBEL S CALE

 In general, the smallest difference in loudness that can be detected by the human ear is 1 dB.  When using the decibel scale, every 3-dB increase in SIL is a doubling in intensity.  A 10-dB increase increases the intensity by 10 times.

D ECIBEL S CALE

I NTENSITY  L OUDNESS  The terms “loudness” and “intensity” do not have the same meaning.  Loudness is a measure of the ear’s response to sound. Two sounds can have equal intensity,  but you may hear one sound as louder than another because your ears can detect it better.

S TANDING W AVES node antinode

S TANDING W AVES

R ESONANCE