Two Homework Questions on Sound Waves

[cmilho10]

I have a couple homework questions that I am having trouble with...any help would be appreciated ASAP!

1.)A tuning fork generates sound waves with a frequency of 238 Hz. The waves travel in opposite directions along a hallway, are reflected by walls, and return. The hallway is 45.0 m in length, and the tuning fork is located 14.0 m from one end. What is the phase difference between the reflected waves when they meet? The speed of sound in air is 343 m/s.

2.)While Jane waits on a railroad platform, she observes two trains approaching from the same direction at equal speeds of 7.60 m/s. Both trains are blowing their whistles (which have the same frequency), and one train is some distance behind the other. After the first train passes Jane, but before the second train passes her, she hears beats having a frequency of 4.30 Hz. What is the frequency of the trains' whistles? (Assume that the speed of sound in air is 343 m/s.)

 

[berkeman]

1. What is the wavelength of the 238Hz sound wave? What is the difference in travel distance for the two different paths?

2. What is the difference in the speeds of the two different sound waves that are making it to Jane? Given that delta-v, what base frequency would give the beat frequency of 4.3Hz?

 

[cmilho10]

1. the wavelength would be v/f=1.44
Is the first path 31.0 m, and the second 45.0 m, or are they both the same?
we were told to use the equation
delta r=(phase constant (phi)/2pi)*wavelength

2. Aren't both sound waves traveling at the same speed?

 

[berkeman]

2. No, not relative to Jane. The sound from the first train is moving back at Jane at the speed of sound minus the speed of the train. The sound from the second train is moving forward at Jane at the speed of sound plus the speed of the train.

 

[fargoth]

i think the speed of sound doesn't change when the submitter is moving, the only effect is the dopler effect... the frequency of the sound from the coming train is higher then from the leaving one...
which cause beats in some low freqeuncy (delta frequency)

 

[berkeman]

i think the speed of sound doesn't change when the submitter is moving, the only effect is the dopler effect... the frequency of the sound from the coming train is higher then from the leaving one...
which cause beats in some low freqeuncy (delta frequency)

Oops, good point. I had a brain fade there for a minute. The compressing and lengthening of the final wavelength of the sound in the air happens at the place where the sound is introduced into the still air. From there on, the speed of the sound wave is dependent just on the air pressure, temperature, etc.

 

[Ouabache]

1. the wavelength would be v/f=1.44
Is the first path 31.0 m, and the second 45.0 m, or are they both the same?
we were told to use the equation
delta r=(phase constant (phi)/2pi)*wavelength

In this part you are told the fork is 14m from one end of the hall. The total length of the hall is 45m. So how far is the fork from the other end of the hall?

You may want to do some dimensional analysis on your equation, so you can predict or double check your units of $\delta r$

In this case you have:
$$\delta r = \frac {\phi}{2 \pi} \lambda$$
$2 \pi$ is in radians (rad)
wavelength $\lambda$ is likely in meters (m)
What are the units for phase constant $\phi$?
It is often expressed in time (secs) ,though could be expressed as an angle (radians)
$\delta r$ would be in $\frac {m-sec}{rad}$ which appears to be awkward units for expressing phase differences. (If $\phi$ were in radians, then $\delta r$ would reduce to fraction of $\lambda$ in meters.)

I also calculated the phase for part 1, however my expression for phase difference is in time (sec) or alternatively as an angle (radians or degrees).