WAVE HW ANSWERS
1) Describe how these properties are similar and different in :
Spring Pendulum and String Waves:
Amplitude in a spring it is distance from rest, in a pendulum it is distance pulled, in a string it is height.
Period in a pendulum it is time per back and forth, in a spring it is time per up and down, in a string wave it is time per (traveling) wave.
Frequency Inverse of period.
Wavelength Not really well defined in a spring or a pendulum, since they donít moveÖ it would be the same as amplitude. In a string wave, it is the distance between waves.
What is the main factor that affects the period in each?
In a pendulum it is the length, in a spring, the mass, in a string wave it is the tightness and the material.
2) A pendulum swings back and forth.
Displacement vs. time
3) I make a sound at a frequency of 500 Hz and notice that the ECHO returns to me 10 sec later from a wall 1500 m away. What is the wavelength of the sound?
F= 500 waves per sec. time to go to wall is 5 sec, distance is 1500 m. Velocity= 1500/5= 300 m/s . v= fλ ,
300 = λ * 500 λ= 300/500= .6 meters
4) Draw a transverse rope wave with a frequency of 3 Hz, and one with a frequency of 6 Hz. What is different about each? The frequency of 3 Hz should have waves that are twice as far apart, the 6Hz waves are closer.
Sec Review 12-3
1) As waves pass by a duck floating on a lake, the duck bobs up and down but remains in essentially one place. Explain why the duck is not carried along by the water medium
The duck bobs but the energy is transferred forward, like a transverse wave.
2) Sketch each of the following waves on a spring that is attached on one end:
a) a pulse wave that is longitudinal
b) a periodic wave that is longitudinal
c) a pulse transverse wave
d) a periodic transverse wave
3) Draw a graph for each one of the waves described in b) and d) and label the y axis of each graph with the appropriate variable. Label the following one each graph: crest, trough, wavelength, amplitude.
4) If the amplitude of a sound wave is increased by a factor of four, how does the energy carried by the sound wave in a given time interval change?
5) The smallest insects that a bat can detect are approximately the size of one wavelength of sound the bat makes. If the bat emits a chirp of frequency of 60 Hz, what is the smallest insect it can detect? (speed of sound is 340 m/s)
v= 340 m/s, f = 60 waves.sec, v=fλ , 340=60λ
1) A piano emits the frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s.
v= 340 m/s, f = 28 waves.sec, v=fλ , 340=28λ
λ=12.14 m to .08 m
2) An FM radio station broadcasts electromagnetic waves at a frequency of 125 MHz. These radio waves have a wavelength of 2.4 m. Find the speed of the radio waves.
f=125,000 waves/sec. λ=2.4 m, v=fλ =300,000 m/s (speed of light!)
5) A tuning fork produces a sound with a frequency of 256 Hz and a wavelength in air 1.35 m.
a) What value does this give for the speed of sound in air?
b) What would be the wavelength of the wave produced by this tuning fork in water in which sound travels at 1500 m/s?
a) f=256 waves/sec. λ=1.35 m, v=fλ =345.6 m/s
b) v= 1500 m/s, f = 256 waves.sec, v=fλ , 1500=256λ