Sound wave questinos my tutor couldnt even figure out

In summary, the conversation involved discussing three problems related to sound waves, including calculating the frequency of waves reflected back to a stationary detector, the altitude of a plane based on the time of its sonic boom reaching a man on the ground, and the speed of a flatcar based on the beat frequency between two trumpet players. The conversation also touched upon the use of the doppler shift formula for these calculations. Ultimately, the third problem was resolved with the realization that the negative sign in the formula needed to be made positive.
  • #1
HobieDude16
70
0
sound wave questions my tutor couldn't even figure out

allright, well, i tried these problems, really thought i knew what i was doing, cause this section has been fairly easy, but i just can't get a couple of them! maybe you guys can help?

1 A stationary motion detector sends sound waves of 0.300 MHz toward a truck approaching at a speed of 32.0 m/s. The speed of sound in the air is 343 m/s. What is the frequency of the waves reflected back to the detector?
______ MHz
my method was to use the whole "f=fo[(v(+-)vo)/(v(+-)vs)] ordeal, using v=343, fo=.3, vo=0, and vs=32
so i worked it out like that, got .330868, wrong answer... my tutor's idea was that its not doplar at all, and just to enter the orig f, .3, but that wasnt right either... i have no idea what i did wrong

2. A plane flies at 1.15 times the speed of sound. Its sonic boom reaches a man on the ground 1.00 min after the plane passes directly overhead. What is the altitude of the plane? Assume the speed of sound to be 330 m/s.
______ m
this one should be easy as well, i did sin(theta)=(1/machnumber) and solving for the angle, then using that, as well as the time (60s) times the speed of sound (330 in this case) to find the hypotenuse of a triangle... did that, solved for the missing side, got 17217.39m, but that's wrong... any ideas?

and lastly
3. A trumpet player on a moving railroad flatcar and a second trumpet player standing alongside the track both play a 440 Hz note. The sound waves heard by a stationary observer between the two players have a beat frequency of 5.0 beats/s. The speed of sound in the air is 343 m/s. What is the flatcar's speed?
_____ m/s
for this one, figured id use the whole "fb=f1-f2" to get the freq, so that owuld be 445 Hz. then plug the numbers into the f=fo[(1/(1-(vc/vs))] with f=445Hz, fo=440Hz, vs=343m/s, and solve for vc... got 3.8539, wrong...

those were all the problems out of about 15 that i couldn't get, and i thought i just didnt grasp the concept, but when my tutor couldn't do them, i figured id ask some other experts for their opinions... any help would be greatly appreciated
 
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  • #2
HobieDude16 said:
1 A stationary motion detector sends sound waves of 0.300 MHz toward a truck approaching at a speed of 32.0 m/s. The speed of sound in the air is 343 m/s. What is the frequency of the waves reflected back to the detector?
There is a double shift because of the reflection. The original sound is doppler shifted up when received by the approaching truck. When it is reflected back to the detector, it is doppler shifted upward again.

2. A plane flies at 1.15 times the speed of sound. Its sonic boom reaches a man on the ground 1.00 min after the plane passes directly overhead. What is the altitude of the plane? Assume the speed of sound to be 330 m/s.
The sound travels along the hypotenuse, so the time of travel is [itex]\Delta t = L_{hyp}/v_{sound}[/itex]. But that time is not 60 seconds. It is 60 seconds + the time it takes for the plane to fly from the opposite end of the hypotenuse to the point directly overhead ([itex]60 + L_{horiz}/v_{plane}[/itex])

3. A trumpet player on a moving railroad flatcar and a second trumpet player standing alongside the track both play a 440 Hz note. The sound waves heard by a stationary observer between the two players have a beat frequency of 5.0 beats/s. The speed of sound in the air is 343 m/s. What is the flatcar's speed?
fb=f1-f2. So the approaching sound wave is doppler shifted to 445 Hz. Use:
[tex]f = f_0 \frac{v_{sound}}{v_{sound} -v_{source}}[/tex]
I get a speed of about 4m/sec.

AM
 
  • #3
well, i got the first 2, a friend helped me out, but the 3rd is still a mystery, you said you got about 4m/sec, which is basically what i got with the 3.85m/s, and i don't think theyd mark it wrong with an exact answer... so that one is still up for grabs on help. thanks for the help though man!
 
  • #4
HobieDude16 said:
well, i got the first 2, a friend helped me out, but the 3rd is still a mystery, you said you got about 4m/sec, which is basically what i got with the 3.85m/s, and i don't think theyd mark it wrong with an exact answer... so that one is still up for grabs on help. thanks for the help though man!
It doesn't say which direction the car is going so there are two potential answers which are slightly different (the doppler shifted frequency would be 435 Hz) and differ by a - sign. So maybe they are looking for both answers.

AM
 
  • #5
ha, that's it, they wanted the negative answer, just make it postive... its negative cause the train is going away! hahaha, thanks man for the help!
 

1. What are sound waves and how do they travel?

Sound waves are vibrations that travel through a medium, such as air, water, or solids. They are created by objects vibrating, which causes the molecules in the medium to vibrate and transfer the energy from one molecule to the next, creating a wave-like motion.

2. How fast do sound waves travel?

The speed of sound waves depends on the medium through which they are traveling. In air at room temperature, sound waves travel at approximately 343 meters per second. In water, sound waves travel at a much faster speed of about 1,500 meters per second.

3. What factors affect the speed of sound waves?

The speed of sound waves can be affected by several factors, including the temperature, density, and elasticity of the medium. In general, the denser and more elastic the medium, the faster sound waves will travel. Temperature also plays a role, as sound waves travel faster in warmer temperatures.

4. How does frequency affect sound waves?

Frequency refers to the number of vibrations per second and is measured in hertz (Hz). Higher frequency sounds have more vibrations per second and are perceived as higher pitched, while lower frequency sounds have fewer vibrations per second and are perceived as lower pitched. Frequency also affects the wavelength and energy of a sound wave.

5. Can sound waves be harmful to humans?

Yes, sound waves can be harmful to humans at high levels. Exposure to loud noise, such as from machinery, concerts, or explosions, can cause temporary or permanent hearing loss. Additionally, certain frequencies of sound waves can cause damage to the inner ear and other parts of the body. It is important to protect your ears from loud noises and limit exposure to harmful sound levels.

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