13 April 2010

Waves

Waves
Problem 1.
A saxophone is playing a steady note of frequency 266 Hz. The temperature in the room is 25 C. Suppose that at some instant the varying pressure at your eardrum is at a maximum. How far away in meters is the next pressure maximum?
Solution: 
The distance between the pressure maxima is an integer number of wavelength. Therefore the shortest distance is the wavelength. The speed of sound at 25 C is 346.33 m/s. Then we can find the wavelength:



Problem 2.
(Inquiry into Physics-5th ed.,Ostdiek,Bord) The quartz crystal used in an electric watch vibrates with frequency 32,768 Hz. What is the period of the crystals motion?
Solution:
 
By definition the frequency is the inverse period (see equations). Then the period is


Problem 3.
A sound wave traveling at 350 m/s has a frequency of 500 Hz. What is its wavelength?
Solution: 
The wavelength is related to the frequency and the speed by the following relation :


Problem 4.
Estimate how far away a cicada can be heard if the lowest possible audible intensity of a sound it produces is and the power of the cicada's sound source is .
Solution: 
We can estimate that the total power of the cicada's sound is distributed uniformly over the spherical surface of radius . Then at distance the intensity of the sound is
The largest radius is achieved when the intensity is . Then
Then


Problem 5.
 
Light of wavelength 497.0 nm appers to have a wavelength of 500.2 nm when it reaches eart from a distance star. find the velocity of the star if the speed of light is 300000000 m/s.


Solution: 
In this problem we need to use the expression for the Doppler shift of the frequency of the wave for an observer moving relative to the source of the waves.. If the source of the light (wave) is moving with a speed then the change in the frequency is
where is the speed of light. Since
Then
and
From this expression we can find the speed of the source