16-8. A person lying on an air mattress in the ocean rises and falls through one complete cycle every five seconds. The crests of the wave causing the motion are 20.0 m apart. Determine (a) the frequency and (b) the speed of the wave.

The period T is the time for one complete cycle, which is given as 5 s. The frequency is related to the period by

f = 1/T = 1/(5 s) = 0.2 Hz

The speed is found from the frequency and the wavelength, which is given as 20.0 m

v = fl = (0.2 Hz)(20.0 m) = 4.0 m/s

16-57. A loudspeaker has a circular opening with a radius of 0.0950 m. The electrical power needed to operate the speaker is 25.0 W. The average sound intensity at the opening is 17.5 W/m². What percentage of the electrical power is converted by the speaker into sound power?

(This is not a topic that is specifically talked about in the text book, but it just needs a few general ideas putting together.)

The intensity, I, is the power/area, P/A, so the total power coming through the circular opening is

P = IA = (17.5 W/m²)p (0.0950 m)² = 0.496 W

Expressed as a percentage of the electrical power consumed by the speaker this is

(0.496 W)/(25.0 W) = 0.0198 = 1.98%

16-66. The sound intensity level of a jet engine is 138 dB, while at a rock concert it is 115 dB. Find the ratio of the sound intensity of the jet engine to the sound intensity of the rock concert.

You could relate each of the intensities to the threshold intensity I₀, but it is not necessary. The ratio of the intensities is related to the difference in the decibel levels.

Decibel level of jet engine - decibel level of rock concert = 138 - 115 = 23 dB

This is related to the ratio of the intensities by

10 log(I_engine/I_concert) = 23

log(I_engine/I_concert) = 2.3

I_engine/I_concert = antilog(2.3) = 10^2.3 = 200