Question

A. What length should an oboe have to produce a fundamental frequency of 244 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

B. What frequency is received by a person watching an oncoming ambulance moving at 119 km/h and emitting a steady 706 Hz sound from its siren? The speed of sound on this day is 333 m/s.

C. What energy in millijoules falls on a 0.808 cm diameter eardrum in 8 hours of exposure to a sound intensity level of 81.3 dB?

D. Dolphins make sounds in air and water. What is the ratio of the wavelength of a sound in air (v_w ≈ 346 m/s) to its wavelength in seawater (v_w ≈ 1,553 m/s)?

E. Find the length of an organ pipe closed at one end that produces a first overtone frequency of 276 Hz when air temperature is 21.3ºC .

Answer 1

A)we know that

f = v/2L

L = v/2f

L = 343/(2 x 244) = 0.703 m

Hence, L = 0.703 m

B)observed frequency will be:

f' = v/(v - vs)f

vs = 119 km/h = 33.1 m/s

f' = 333/(333 - 33.1)706

f' = 783.66 Hz

C)I = 81.3 dB = 0.00013 W/m^2 ; d = .808 cm => r = 0.404 cm ; 8 hrs = 2.88 x 10^4 s

I = P/A

P = I A

P = 0.00013 x 3.14 x 0.00404^2 = 6.66 x 10^-9 W

E = P t

E = 6.66 x 10^-9 x 2.88 x 10^4 = 1.91 x 10^-4 J

Hence, E = 1.91 x 10^-4 J

D)lambda(air)/lambda(water) = v(air)/v(water)

lambda(air)/lambda(water) = 346/1553 = 0.223

Hence, lambda(air)/lambda(water) = 0.223