INDIANA UNIVERSITY, DEPT. OF PHYSICS P105, Basic Physics of Sound, Spring 2010

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1 Name: Joe E. Physics ID#: INDIANA UNIVERSITY, DEPT. OF PHYSICS P105, Basic Physics of Sound, Spring 2010 Midterm Exam #1 Thursday, 11 Feb. 2010, 7:30 9:30 p.m. Closed book. You are allowed a calculator There is a Formula Sheet at the back of the exam that you can gently tear off. Fill in the answers on the exam sheets themselves. If you run out of room, use the back of the sheets. In some cases partial credit is awarded try not to leave blank answers 1. (4 pts) What is sound, and what is the science of sound called? What kind of a wave is a sound wave? Sound is the disturbance in a medium (gas such as air, liquid, solid) represented by oscillations or variations of pressure. The science of sound is called acoustics. A sound wave is a longitudinal wave. 2. (6 pts) Fill in the blanks in the table below: "Physics" Quantity Frequency Amplitude Wave Shape "Perceived" (by ear & brain) Quantity Pitch Volume or Loudness Timber or tone quality 3. (a) (3 pts) The speed of sound at 20 C is 343 m/s. What is the wavelength of a sound wave with a period of 120 µs? f = 1/T λ = v/f = 1/( s) = (343 m/s)/(8,333 Hz) = 8,333 Hz = m = 4.2 cm 1

2 (b) (2 pts) This same sound wave travels through a window with dimensions of 1 m 1 m. Will the wave spread substantially, i.e., will diffraction be important in this case? Give your reason why. λ = m, and d = 1 m; in this case, λ << d, so diffraction will not be important and the wave will not spread substantially. 4. A piano wire of length L = 2.0 m is fixed at both ends inside a grand piano as shown below. (a) (3 pts) Sketch below how the fourth harmonic, f 4, wave or standing wave pattern would appear. Label the nodes and antinodes with "N" and "A", respectively. (b) (3 pts) What is the wavelength, λ 4, of the wave forming this standing wave pattern? Either by inspection, λ 4 = 1.0 m, or λ n = 2L/n ; λ 4 = 2(2.0 m)/4 = 1.0 m (c) (4 pts) If mass of the piano wire vibrating as shown is 20 g, and it is oscillating at the fourth harmonic frequency of f 4 = 260 Hz, what is the tension, T, in the wire? (A) 19.6 N; Mass per unit length, µ = m/l = (0.020 kg)/(2.0 m) = 0.01 kg/m (B) 104 N; (C) 338 N; f n = (n/2l) sqrt(t/µ); 2Lf n /n = sqrt(t/µ) (D) 676 N; (2Lf n /n) 2 = T/µ (E) 1012 N. T = µ(2lf n /n) 2 = (0.01 kg/m)((2)(2.0 m)(260 Hz)/4) 2 = 676 N (d) (2 pts) What would be the fundamental frequency, f 1, of this wire? f 4 = 4 f 1 ; f 1 = f 4 /4 = (260 Hz)/4 = 65 Hz (e) (2 pts) Resonance is the phenomenon where the amplitude of the string above would grow in size if the wire is "driven" at a frequency close to the fundamental frequency. 2

3 5. Prof. Van Kooten is walking back and forth at the front of the class, with his motion as described in the plot below Time (s) (a) (3 pts) During a part of his motion, his velocity is positive. The velocity during this time interval is: (A) 0.23 m/s; (B) 0.67 m/s; (C) 0.75 m/s; (D) 0.83 m/s; (E) 1.50 m/s. Speed = Δx/Δt = rise/run = (3 m ( 2 m))/(13 s 7 s); = (5 m)/(6 s) = 0.83 m/s (b) (2 pts) Over what time range does he stop walking and is writing on the board? (fill in) 3 s to 7 s 6. (2 pts) When a low-flying airplane travels faster than the speed of sound, a shock wave can cause a sonic boom (two words) heard by an observer on the ground caused by constructive interference of wavefronts collecting along a cone-shape with the airplane at its apex. 7. (3 pts) Prof. Van Kooten is on a trans-atlantic flight to the Large Hadron Collider. A pressure of 25 Pa is being exerted by air on one of his eardrums. If the area of his eardrum is 0.55 cm 2, what is the perpendicular force F perp being exerted by the air on the eardrum? P = F perp /A; 0.55 cm 2 ((1 m)/(100 cm)) 2 = m 2 F perp = PA = (25 Pa)( m 2 ) = N 3

4 8. (a) (3 pts) On a frigid day when the temperature is 10º C, you stand 250 ft. (note the archaic units here!) away from a canyon wall and scream "Geez, its' cold!". How long does it take for you to hear the echo? 0.47 s. d = 250 ft ((1 m)/3.281 ft) = 76.1 m. Total distance for echo (there and back), D = 2d v sound = ( ( 10)) m/s = m/s t = D/v = (2)(76.1 m)/(325.3 m/s) = 0.47 s (b) (2 pts) The temperature 100 m higher is a relatively balmy 0º C. In this case, what happens to the wavefront of your scream, why, and what is this effect called? The wavefront of the scream will bend downwards since the temperature is higher up, resulting in a higher velocity of sound. This effect is called refraction. 9. The graph below shows the position (y) versus time (t) plot of a mass on a large spring, similar to that we encountered in lecture. The mass is pulled and released to give the indicated amplitude (from equilibrium position). (a) (3 pts) If the spring constant of the spring is k = N/m, and the mass is m = 2.0 kg, what is the frequency of the oscillation? f = 1/(2π) sqrt(k/m) = 1/(2π) sqrt(( N/m)/(2.0 kg)) = 4.0 Hz (b) (2 pts) With this information, fill in the appropriate values on the time axis. To fill in the time axis, need to know the period! T = 1/f = 1/(4.0 Hz) = 0.25 s A lot of students incorrectly filled in the frequency on the time axis. 4

5 (c) (3 pts) Indicate on the graph when the kinetic energy of motion, i.e., KE would be equal to zero. What is the total mechanical energy of this oscillation? Since KE = (1/2)mv 2, KE = 0 when v = 0. This occurs when the tangent to the sine curve is zero, at the indicated points (maximum point of excursion in either direction). Can find total energy = PE + KE. When KE = 0, Total energy = PE = (1/2)kx 2 Total energy = (1/2)( N/m)(0.05 m) 2 = 1.58 J (d) (2 pts) Such sinusoidal motion is called simple harmonic motion (two words). (e) (2 pts) When the spring is extended a distance of 5.0 cm beyond its position of equilibrium, what is the force of the spring on the mass? F = k Δx = ( N/m)( 0.05 m) = 63.1 N (f) (2 pts) If we wanted to increase the frequency of the oscillation for the same size mass, would we need a stiffer or weaker spring? f = 1/(2π) sqrt(k/m), therefore to increase f, need to increase k. To increase k, need a stiffer spring. 10. Consider the square wave A and the triangular wave B shown below. (a) (2 pts) The frequency of wave B is 2 times that of wave A, and the amplitude of wave B is 0.5 times that of wave A. (b) (4 pts) Sketch the sum of the two waves (on the same axes). (c) (2 pts) What is the frequency of the sum A+B of the waves? 0.25 Hz. Pattern repeats itself every T = 4.0 s. f = 1/T = 1/(4.0 s) f = 0.25 Hz 5

6 What is the amplitude of the sum A+B of the waves? 3.0 Pa. 11. (2 pts) In the following musical instruments indicate what it is that vibrates: a violin (string), a drum (membrane_), a marimba (bar ), and an organ (air column). 12. The figure below shows wavefronts (solid lines) spreading out from a moving source "S". (a) (1 pt) In which direction is the source moving? (right-to-left or left-to-right)? From right-to-left. (b) (1 pt) Will an observer at A or B hear a lower pitch? Lower pitch implies lower frequency. Lower frequency means longer wavelength. From the distances between crests, the wavelengths heading towards B are longer. B therefore hears a lower pitch. 6