9-B19 (Somewhat revised) . A point on a horizontal vibrating piano string is moving up and down in SHM, which is to say that position, velocity, and acceleration undergo sinusoidal oscillation. 

Given: The frequency is 256 Hz and the amplitude is 1.1 mm.

Find (a) What is the maximum vertical velocity of that point on the string? (Hint: Remember the relationship between SHM and circular motion.)
(1.77 m/s)

(b) What is the maximum acceleration of that point on the string?
(2.8E3 m/s^2)

9-1 A boy takes his sister to the park to use the swings. Although they usually use the little swing set, they decide to use the big swings today.

Given: They are interested in what the period will be on the big 6.13m swings. The period of the little swings was 2.8s when the boy was swinging. The boy weighs 321N, and his younger sister weighs 289N.

Find (a) What will be the period of the boy on the big swings?
(5.0 s)

(b) What will be the sister’s frequency on the big swings?
(0.20 Hz)

(c) What was the length of the little swings?
(1.96 m)

10-B13 (Somewhat revised, but the numbers are the same.) . During the cold war, radio broadcasts were used to win the hearts and minds of the people. Propaganda they called it. A government that didn't want their people to hear a particular broadcast would jam it with a signal that was close to, but not identical to, the broadcast signal so as to produce beats.

Given: The speed of light is 2.99793E8 m/s. Propaganda is broadcast at 91.700 MHz while the jamming signal is broadcast at 91.702 MHz.

Find (a) What is the wavelength of the propaganda signal?
(3.26928 m  Yes, everything is known to 5 significant figures, so 6 is justified in this case.)

(b) How many beats per second are heard?
(2 kHz  But now we are down to 2 significant figures because we subtracted. The rule of thumb only works for multiplying and dividing.)

10-A15 (Somewhat revised) Bats use ultrasonic sound waves to locate insects to eat. They can actually tell both the position and size of the insect by the reflected sound after they have emited an ultrasonic chirp. When the wavelength matches the size of a particularly juicy insect the reflected sound is maximum.

Given: On a day when the speed of sound is 344 m/s, a bat chirps at a frequency that changes from 44,000 Hz to 22,000 Hz, looking for a 1.1 cm mosquito.

Find (a) What is the shortest wavelength emitted by the bat?
( 0.782 mm)

(b) At what frequency will the wavelength match the size of the mosquito?
(31 kHz)

11-A10 (Somewhat revised, but the numbers are the same) . An Exploratorium exhibit, called the Pipes of Pan, features a series of  pipes open at both ends. A rubber flapper is provided so that a visitor can close one end of a pipe, thus changing its resonate frequency.

Given: One of the pipes is 86 cm long. On a day when the speed of sound is 344 m/s, you decide to close one end of the pipe.

Find (a) What is the fundamental frequency of the pipe  when it is open at both ends?
(200 Hz)

(b) What is the fundamental frequency of the pipe  when it is open at one end and closed at the other?
(100 Hz)

11-B23 (Somewhat revised to bring the environment closer to home and add some helpful hints) .Wishing to be near the perpetual party on Dixon Street, a sophomore physics major takes a lease on an apartment next to The Eat Place, only to discover that physics is something that is done late at night. Soundproofing the living room helps some, so long as the band next door keeps it down just a little.

Given: The student finds that physics can be done at 63 dB, which is actually twice as loud as a Sunday morning 60 dB when Dixon Street is quiet. Heavy duty soundproofing is advertised to produce a noise reduction of 33 dB. The threshold of hearing is usually taken as 1E-12 W/m^2. With no insulation, the intensity of sound in the apartment is 2E-3 W/m^2.

Find (a) What is the sound level in the apartment with no insulation when measured in dBs?
(93 dB)

(b) Will the soundproofing allow physics to be done while the band plays on?
(60 dB)