1© Manhattan Press (H.K.) Ltd. 10.8 Quality of sound

© Manhattan Press (H.K.) Ltd. 1

10.8 Quality of sound10.8 Quality of sound


10.8 Quality of sound (SB p. 158)

Quality of sound

Notes of same frequency by different musical instruments sound different to us

The quality of a note refers to its waveform.

Violin Pipe organ Go to

More to Know 1More to Know 1



Quality of sound

Note is formed by- its fundamental frequency (pitch of note)- it is added with other frequencies (overtones) of different amplitudes- resultant waveform different- different sound quality


10.1 10.1 IntroductionIntroduction

1. Stationary waves on a rope can be produced if we tie one end of the rope to a wall and move the free end up and down continuously. The superposition of the incident wave and the reflected wave produces the stationary (or standing) wave in the rope.





2. For a stationary wave, the parts remain stationary are called nodes (N) and the parts vibrating with the largest amplitude are called antinodes (A).

3. Using the principle of superposition of waves, the resultant wave can be represented by: y = A sintwhere A = 2a cos .

x2




4. At nodes, the amplitude is always zero and hence A = 0. We have:and the distance between two successive nodes is .

5. At antinodes, the amplitude is maximum and equals 2a. We have:The distance between two successive antinodes is also .

,...,,x4

54

34

2

,...,,x 2

0

2


10.1 10.1 IntroductionIntroduction6. The comparison between progressive and

stationary waves:


Progressive wave Stationary wave

Energy is transferred along the direction of propagation.

No energy is transferred along the direction of propagation.

The wave profile moves in the direction of propagation.

The wave profile does not move in the direction of propagation.

Every point along the direction of propagation is displaced.

There are points known as nodes where no displacement occurs.

Every point has the same amplitude.

Points between two successive nodes have different amplitudes.

Neighbouring points are not in phase.

All points between two successive nodes vibrate in

phase with one other.


10.2 10.2 Stationary waves on a stretched stringStationary waves on a stretched string


7. Stationary waves of various frequencies can be set up in a stretched wire of length ().λ0 = 2 where λ0 is the wavelength of the stationary wave vibrating at its fundamental frequency (f0).

8. The speed v of a transverse wave on a stretched wire depends on the tension (T ) of the wire and the mass per unit length (μ) of the wire:

2ovf

Tv


10.3 10.3 Stationary waves in airStationary waves in air

9. For a stationary wave in air: v = 2fdwhere d is the distance between two successive antinodes.



10.4 10.4 Stationary waves in a closed pipeStationary waves in a closed pipe

10. Sound can be produced by stationary waves formed in an open pipe (both ends open) or a closed pipe (one end open and another end closed). If a sound wave travelling from the open end is reflected at the closed end of the pipe, a stationary longitudinal wave is formed.



10.4 10.4 Stationary waves in a closed pipeStationary waves in a closed pipe


11. For the fundamental note:

where is the length of the tube, λ0 is the wavelength, v is the velocity of sound in air. Notes of frequency f0, 3f0, 5f0,..., or the odd harmonics are obtainable.

4 and

4 oo vf


10.5 10.5 End correctionEnd correction


12. For the stationary waves formed in a closed pipe:(a) For the fundamental note, ( + c) =(b) For the first overtone, ( + c) = (c) For the second overtone, ( + c) =

4o

143

245


10.6 10.6 Resonance tube: Measurement of Resonance tube: Measurement of speed of sound in airspeed of sound in air


13. For the graph of against 1, the speed of

sound in air (v) = .

f1

graph ofGradient 4


10.7 10.7 Stationary waves in an open pipeStationary waves in an open pipe


14. For an open pipe with both the ends open, a stationary wave can be set up by blowing across the upper open end of the pipe. We have:

vf2o


10.8 10.8 Quality of soundQuality of sound15. The notes of the same frequency produced

by different musical instruments sound different to us. It is because different musical instruments produce notes of different waveforms.

16. In general, a note is formed by its fundamental frequency, which characterizes the pitch of the note. This frequency is often added with other frequencies (overtones). This makes the resultant waveform different and results in different sound quality.





End



A vibrating source and a

medium for propagation are

the two necessary conditions

for sound waves to

propagate. Return to

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1© Manhattan Press (H.K.) Ltd. 10.8 Quality of sound