Sound waves ：練習問題

A point source of sound emits longitudinal waves uniformly in all directions in a non-absorbing medium. An observer at a distance \(r\) from the source measures a sound intensity level of \(L_1 = 70.0 \text{ dB}\). The observer then moves to a new distance \(r'\). At the same time, the amplitude of the pressure variation at the source is increased by a factor of \(\sqrt{10}\). If the sound intensity level measured at the new distance \(r'\) is now \(L_2 = 66.0 \text{ dB}\), what is the ratio of the new distance to the original distance \(\frac{r'}{r}\)?

(Given: \(\log_{10} 2 \approx 0.301\))

A point source of sound emits energy uniformly in all directions in a non-absorbing medium. A sound level meter at a distance \(r\) from the source measures a sound intensity level of \(L_1 = 80.0 \text{ dB}\). The observer then moves to a new distance \(r'\). Simultaneously, the power output of the source is changed such that the amplitude of the pressure variation at the source is tripled. If the new sound intensity level measured at \(r'\) is \(L_2 = 72.0 \text{ dB}\), what is the ratio of the new distance to the original distance \(\frac{r'}{r}\)?

(Given: \(\log_{10} 2 \approx 0.301\), \(\log_{10} 3 \approx 0.477\))

A point source of sound emits sound energy uniformly in all directions in a non-absorbing medium. A small detector is placed at a distance \(r\) from the source and measures a sound intensity level of \(L\). The source power is then doubled, and the detector is moved to a new position such that the new sound intensity level is \(L + 10 \text{ dB}\). What is the new distance of the detector from the source in terms of \(r\)?

(Given: \(\log_{10} 2 \approx 0.301\))

A musician plays a musical instrument which can be modeled as a point source of sound emitting waves uniformly in all directions in a non-absorbing medium. An observer initially at a distance of \(10.0 \text{ m}\) from the source measures a sound intensity level of \(75.0 \text{ dB}\). The musician then increases the power of the source by a factor of \(12\). Simultaneously, the observer moves to a new distance such that the amplitude of the pressure variation of the sound wave at the new position is twice the amplitude at the original position before the power was increased. What is the new sound intensity level measured by the observer?

(Given: \(\log_{10} 2 \approx 0.301\), \(\log_{10} 3 \approx 0.477\))

A point source of sound emits waves uniformly in all directions in a non-absorbing medium. An observer at a distance \(r\) from the source measures a sound intensity level of \(L_1 = 70.0 \text{ dB}\). The observer then moves to a new distance \(r'\). Simultaneously, the power output of the source is increased such that the amplitude of the pressure variation at the source is doubled. If the amplitude of the pressure variation at the new distance \(r'\) is measured to be \(1.5\) times the original amplitude measured at distance \(r\) (before the power was increased), what is the new sound intensity level \(L_2\) and the ratio of the distances \(\frac{r'}{r}\)?

(Given: \(\log_{10} 2 \approx 0.301\), \(\log_{10} 3 \approx 0.477\))

Two musical instruments play the same note with identical pitch and loudness, yet they sound distinct to a listener. Explain the physical basis for this difference in quality (timbre) in terms of wave superposition.

Calculate the percentage of ultrasound intensity reflected at a boundary between two biological tissues if the acoustic impedance of the second tissue \(Z_2\) is exactly \(1.2\) times the acoustic impedance of the first tissue \(Z_1\). Use the intensity reflection coefficient formula \(\alpha = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}\).

A specific musical instrument produces a sound with a frequency of \(440 \text{ Hz}\). If the sound wave enters a medium where the wave speed increases by \(10\%\) while its intensity remains constant, explain the effect on the pitch and the wavelength of the sound as perceived within the new medium.

Two loudspeakers, S{_1}{_} and S{_2}{_}, are connected to the same audio generator and produce sound waves in phase. They are placed \(2.0 \text{ m}\) apart. A listener walks along a line parallel to S{_1}{_}S{_2}{_}, at a perpendicular distance of \(10 \text{ m}\) from the midpoint of S{_1}{_}S{_2}{_}. The speed of sound in air is \(340 \text{ m s}^{-1}\) and the frequency of the sound emitted by the loudspeakers is \(680 \text{ Hz}\).

(a) Calculate the wavelength of the sound waves produced.

(b) Explain how the listener would experience alternating loud and quiet sounds as they walk along the line, referring to the principle of superposition.

(c) If the frequency of the sound generator is increased, describe how the spacing between the loud regions would change.

Two small loudspeakers, \(P\) and \(Q\), are connected to the same signal generator and are placed \(4.0 \text{ m}\) apart in an open space. They emit sound waves in phase with an initial frequency of \(500 \text{ Hz}\). The speed of sound in air is \(340 \text{ m s}^{-1}\). A microphone is placed at point \(X\), which is located \(5.0 \text{ m}\) from \(P\) and \(5.5 \text{ m}\) from \(Q\).

(a) Calculate the wavelength of the sound waves emitted by the speakers.

(b) Determine the path difference of the sound waves reaching point \(X\) and state, with a reason, whether the interference at \(X\) is constructive, destructive, or neither.

(c) The frequency of the signal generator is slowly increased from \(500 \text{ Hz}\). Calculate the first frequency at which the microphone at \(X\) will detect a maximum sound intensity.

(d) If the loudspeakers are now adjusted to be \(180^\circ\) out of phase while keeping the frequency constant at \(500 \text{ Hz}\), describe the change in the sound heard by an observer moving along the perpendicular bisector of the line joining \(P\) and \(Q\). Justify your answer using the principle of superposition.