(a) State the three characteristics of sound and the factor on which each of them depends.
(b) Explain resonance as applied to sound.
(c) What role does echo play in the construction of a concert hall?
(d) The surface of an ear drum (assumed circular) has a radius 2.1 mm. It resonates with an amplitude of 0.8 x 10\(^{-7}\) in as a result of impulses received from an external body vibrating at 2400 Hz. If the resulting pressure change on the ear drum is 3.6 x 10\(^{-5}\) NM\(^{-2}\), calculate the:
(i) period of oscillation;
(ii) velocity;
(iii) acceleration;
(iv) force. [\(\pi\) = 3.14 ].
Explanation
(a) Characteristics of sound and their corresponding Factors
|
Characteristics |
factors |
|
- Pitch - Timber or quality - Loudness or intensity |
- Frequency - Harmonics or Overtone - Amplitude |
(b) Resonance is a phenomenon which occurs when an external vibrating source of sound such as a sounding tunning fork set another system such as molecules of column into vibration; at a stage the system vibrates with maximum amplitude producing, a loud sound.
(c) Echo enables the construction engineers to line the interior wall with sound absorbing materials to prevent echo.
(d)(i) Period T = \(\frac{1}{f} = \frac{1}{2400} = 4.2 \times 10^{-7}\)
= 1.2 x 10\(^{-3}\)ms\(^{-1}\)
(ii) Velocity V = \(\omega r = 2 \pi fr\)
= 2 x 3.142 x 2400 x 0.8 x 10\(^{-7}\)
= 1.2 x 10\(^{-3}\)ms\(^{-1}\)
(iii) Acceleration a = \(\omega^2r\)
= (\(2 \pi f)^2r = (2 \times 3.14 \times 2400)^2 \times 0.8 \times 10^{-7}\)
= 18.2 ms\(^{-2}\)
(iv) p = \(\frac{F}{A}\)
force F = PA
= 3.6 x 10\(^{-5} \times 3.14 \times (2.1 \times 10^{-3})^2\)
= 5.0 x 10\(^{-11}\) N