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

2 © Manhattan Press (H.K.) Ltd 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 1 More to Know 1

3 © Manhattan Press (H.K.) Ltd Quality of sound (SB p. 158) 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

4 © Manhattan Press (H.K.) Ltd Introduction 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 Quality of sound (SB p. 159)

5 © Manhattan Press (H.K.) Ltd Introduction 10.8 Quality of sound (SB p. 159) 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 sin  t where A = 2a cos.

6 © Manhattan Press (H.K.) Ltd Introduction 10.8 Quality of sound (SB p. 159) 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.

7 © Manhattan Press (H.K.) Ltd Introduction 6. The comparison between progressive and stationary waves: 10.8 Quality of sound (SB p. 159) Progressive waveStationary 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.

8 © Manhattan Press (H.K.) Ltd Stationary waves on a stretched string 10.8 Quality of sound (SB p. 160) 7. Stationary waves of various frequencies can be set up in a stretched wire of length ( ). λ 0 = 2  where λ 0 is the wavelength of the stationary wave vibrating at its fundamental frequency (f 0 ). 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:

9 © Manhattan Press (H.K.) Ltd Stationary waves in air 9. For a stationary wave in air: v = 2fd where d is the distance between two successive antinodes Quality of sound (SB p. 160)

10 © Manhattan Press (H.K.) Ltd Stationary 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 Quality of sound (SB p. 160)

11 © Manhattan Press (H.K.) Ltd Stationary waves in a closed pipe 10.8 Quality of sound (SB p. 160) 11. For the fundamental note: where  is the length of the tube, λ 0 is the wavelength, v is the velocity of sound in air. Notes of frequency f 0, 3f 0, 5f 0,..., or the odd harmonics are obtainable.

12 © Manhattan Press (H.K.) Ltd End correction 10.8 Quality of sound (SB p. 160) 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) =

13 © Manhattan Press (H.K.) Ltd Resonance tube: Measurement of speed of sound in air 10.8 Quality of sound (SB p. 160) 13. For the graph of against 1, the speed of sound in air (v) =.

14 © Manhattan Press (H.K.) Ltd Stationary waves in an open pipe 10.8 Quality of sound (SB p. 160) 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:

15 © Manhattan Press (H.K.) Ltd Quality of sound 15. 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 Quality of sound (SB p. 160)

16 © Manhattan Press (H.K.) Ltd Quality of sound (SB p. 161)

17 © Manhattan Press (H.K.) Ltd. End

18 © Manhattan Press (H.K.) Ltd Quality of sound (SB p. 158) A vibrating source and a medium for propagation are the two necessary conditions for sound waves to propagate. Return to Text