Question

3. (a) The range of audible frequencies of sound in air, assuming sufficient amplitude, is from about 20 Hz to 20, 000 Hz. What is the range of audible wavelengths? Take the speed of sound in still air to be v = 344m/s.

(b) Sound is detected when the eardrum is caused to vibrate. The diameter of the eardrum is about 10 mm. Suppose a person whispers into your ear with an intensity, I = 10−8 W/m2 = E/(At), where E is the energy delivered to your eardrum, A is the area of the eardrum, and t is the duration of the whisper. i. What is the decibel level of the whisper ? ii. Calculate the area of the eardrum. How much energy, E, is delivered to the eardrum during 1 minute of the whisper ?

(c) A 1.5 metre long rope is stretched between two supports with a tension that gives a speed of transverse waves of 48 m/s. What is the wavelength and frequency of: i. the fundamental frequency? ii. the fourth harmonic?

(d) Two swift canaries fly towards each other, each moving at 15m/s relative to the ground, and each warbling a note of frequency 1,750Hz. i. What frequency does each canary hear from the note of the other? ii. What wavelength will each canary measure for the note of the other?

Answer 1