1. A bat produces a spherical sonar pulse with an power of 0.020 W. There is a bug 5.0 m away that has a cross sectional area of 100 mm². Assuming the bug also acts as a spherical source for the reflection, what will be the intensity of the reflection when it reaches the bat? Assume that the bug reflects all of the sound it intercepts and that the separation of bat and bug remains constant.
2. Volcanic eruptions are loud. Big eruptions can be heard hundreds of kilometres away. Suppose you just hear an eruption that is 100 km away. Typically a person might notice a sound of about 1 × 10^-8 W/m² while outside. What would be the intensity at 100 m?

3. The human ear canal is approximately a cylindrical tube of length 2.5 cm. Find the fundamental resonant frequency?

4. Having no ruler at hand, you decide to determine the length of a hollow open-ended tube by holding one end next to a sound source and varying the frequency of the sound. The lowest frequency that causes resonance in the tube is f = 420 Hz. Assuming that the speed of sound is 343 m/s, what is the length of the tube? Sketch the standing wave.
5. A narrow hollow tube of length L = 3.50 m is open at both ends and sits on two sawhorses. A wind is blowing and the tube is "moaning". What is the lowest possible frequency for the sound produced? Sketch the standing wave. Take the speed of sound to be 340 m/s.
   
   
6. As shown in the diagram below, a speaker plays a single frequency sound. On its way to you, some of the sound echoes (reflects) off a wall. As a result, the sound is quieter than it should be.
   (a) If the wall is flexible, what is the lowest frequency that creates the lowest sound intensity at your position?
   (b) If the wall is stiff, what is the lowest frequency that creates the lowest sound intensity at your position?
   
   
7. Two in-phase loudspeakers are located 3.00 m apart on the stage of an auditorium. A detector is placed 20.0 m from one speaker and 21.2 m from the other. What is the lowest note for which destructive interference is a maximum? What is the lowest note for which constructive interference is a maximum? The speed of sound in air is 343 m/s. The signal generator now flips the phase of the nearer speaker by 180°, how do your answers above change?
8. When one student is doing an exam in an otherwise very quiet room, the sound level is 45 dB. What is the intensity of the noise produced by the student? If there are 30 equally noisy students in the room, and assuming that you are the same distance from all the students, what would the new sound level be?

9. You've been out very late and when you come home your parents are very angry and start shouting at you. This upsets the family dog who starts howling. The diagram below shows their positions with you in the middle. The distances are r_DAD = 1.20 m, r_MOM = 1.35 m, and r_DOG = 2.00 m. The power in their voices are respectively, P_DAD = 1.25 mW, P_MOM = 0.85 mW, and P_DOG = 1.00 mW. Find the intensity of sound from each source at your position. Treat the sources as incoherent (in the physical sense) and find the sound level. Be sure to include the effects of the normal background sound level of 60 dB. I₀ = 10^-12 W/m².
10. The beat frequency between an unknown tuning fork and a 500 Hz tuning fork is 12 Hz. Compared with a 504 Hz tuning fork, the beat frequency is 16 Hz. What is the frequency of the unknown tuning fork?
11. A driver travels north on a highway at a speed of 25 m/s. A police car, driving south at a speed of 40 m/s, approaches with its siren sounding at a base frequency of 2500 Hz. (a) What frequency is heard by the driver as the police car approaches? (b) What frequency is heard by the driver after the police car passes him? If the driver had been travelling south, what would your results have been for (a) and (b)? The speed of sound in air is v = 340 m/s.
12. Owls, night hunters like bats, also use echolocation to find prey but it is passive not active as the owls are not emitting the sound. Discuss how this difference, and the requirement for some light to see, affects the hunting strategy of owls with respect to bats?
13. In sonar, an intermittent high frequency sound pulse is broadcast in all directions. The sound is reflected from solid objects and returns to broadcaster. The time it took for the echo to return and the direction from which the echo came are used to locate nearby objects. This is Echo Location. By measuring the Doppler Shift of the echo, the speed of the object can be found. There is an added complication in that the Doppler Shift occurs twice, once from the source to the receiver, and then from the receiver (now a source of the echo) back to the original source (which is now a receiver of the echo). The echo will have a frequency
    
    f' = f₀ [(1 ± u_r/v)/(1 ± u_s/v][(1 ± u_s/v)/(1 ± u_r/v)] .

    A submarine traveling at 17 km/h sends out pulses at 38.7 MHz. The delay in the echo off a second sub has been rapidly decreasing and is currently 75 ms. How far apart are the two subs? If the second sub is moving at 22 km/h, what is the frequency of the returned echo? The speed of sound in seawater is 1.54 km/s.

Questions? mike.coombes@kwantlen.ca