Can you help with these sound wave problems?

[lavafrog]

Help With Sound Wave Problems!

Hi...I'm studying for a test on soundwaves tomorrow, and I have questions on a few problems my teacher never reviewed. I'd appreciate it if someone could even answer one of them. Thanks!

1) At rest, a car's horn sounds the note A (440Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one third the car's speed hears a frequency of 415. How fast is the car moving? Is the bicyclist ahead of or behind the car? T=20C. (Based on the fact that the biker hears a lower frequency than the actual frequency, I've determined that he's behind the car.)

I've found the velocity of sound in these conditions to be 343m/s. Then I used this equation: (f'=frequency heard, f=actual frequency, v=velocity of sound in air, vo=velocity of observer, vs=velocity of the source, or car, +/- is used because it's - on top and + on bottom when the source is going away from you, and + on top and - on bottom when it's coming towards you.)

f'=f(v+/-vo/v+/-vs)

415Hz=440Hz(343m/s-(1/3)vs/343m/s+vs) (Sorry I can't write it out any neater than that, but I don't know how to use the right symbols.)

When I solve the equation for vs, I get 15.35m/s, but the answer is supposed to be 31m/s! Why am I off by a factor of two?

2) The frequency of a steam train whistle as it approaches you is 522Hz. After it passes you, it's 486Hz. How fast was the train moving? (assume constant velocity.)

522-486=36, 36/2=18.
486+18=504Hz. when right in front of you.

522Hz=504Hz(340m/s+0m/s/340m/s-Xm/s) When I solved for x, I got 13m/s. Is this the right answer?


One more I can't even start working on:

Two tuning forks are held near each other and a beat frequency of 6Hz is percieved. if one fork has a f=512Hz, what frequencies are possible for the other?

 

[abercrombiems02]

Hi...I'm studying for a test on soundwaves tomorrow, and I have questions on a few problems my teacher never reviewed. I'd appreciate it if someone could even answer one of them. Thanks!

1) At rest, a car's horn sounds the note A (440Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one third the car's speed hears a frequency of 415. How fast is the car moving? Is the bicyclist ahead of or behind the car? T=20C. (Based on the fact that the biker hears a lower frequency than the actual frequency, I've determined that he's behind the car.)

I've found the velocity of sound in these conditions to be 343m/s. Then I used this equation: (f'=frequency heard, f=actual frequency, v=velocity of sound in air, vo=velocity of observer, vs=velocity of the source, or car, +/- is used because it's - on top and + on bottom when the source is going away from you, and + on top and - on bottom when it's coming towards you.)

f'=f(v+/-vo/v+/-vs)

415Hz=440Hz(343m/s-(1/3)vs/343m/s+vs) (Sorry I can't write it out any neater than that, but I don't know how to use the right symbols.)

When I solve the equation for vs, I get 15.35m/s, but the answer is supposed to be 31m/s! Why am I off by a factor of two?

2) The frequency of a steam train whistle as it approaches you is 522Hz. After it passes you, it's 486Hz. How fast was the train moving? (assume constant velocity.)

522-486=36, 36/2=18.
486+18=504Hz. when right in front of you.

522Hz=504Hz(340m/s+0m/s/340m/s-Xm/s) When I solved for x, I got 13m/s. Is this the right answer?


One more I can't even start working on:

Two tuning forks are held near each other and a beat frequency of 6Hz is percieved. if one fork has a f=512Hz, what frequencies are possible for the other?

To get you started on the last one, consider the following case:

If 1 tuning fork has a frequency of 5 hz and a second one has a tuning frequency of 8 hz, then you would hear a beat frequency of 3 hz. So, the beat frequency is related to the difference of each of the individual frequencies. Likewise if a 5 hz tuning fork and a 2 hz truning fork were placed near each other, you would also hear a beat freuency of 3 hz.

 

[nrqed]

Hi...I'm studying for a test on soundwaves tomorrow, and I have questions on a few problems my teacher never reviewed. I'd appreciate it if someone could even answer one of them. Thanks!

1) At rest, a car's horn sounds the note A (440Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one third the car's speed hears a frequency of 415. How fast is the car moving? Is the bicyclist ahead of or behind the car? T=20C. (Based on the fact that the biker hears a lower frequency than the actual frequency, I've determined that he's behind the car.)

I've found the velocity of sound in these conditions to be 343m/s. Then I used this equation: (f'=frequency heard, f=actual frequency, v=velocity of sound in air, vo=velocity of observer, vs=velocity of the source, or car, +/- is used because it's - on top and + on bottom when the source is going away from you, and + on top and - on bottom when it's coming towards you.)

f'=f(v+/-vo/v+/-vs)

415Hz=440Hz(343m/s-(1/3)vs/343m/s+vs) (Sorry I can't write it out any neater than that, but I don't know how to use the right symbols.)

When I solve the equation for vs, I get 15.35m/s, but the answer is supposed to be 31m/s! Why am I off by a factor of two?

the bike is behind the car (since tje frequency heard is lower) So your sign in the numerator shoudl be a + not a minus.

 

[lightgrav]

The bike encounters 415 waves/s, as it moves into the waves;
so the wavelength in the air must be
lambda = (v_sound + v_bike)/415 [wave/s] .
The waves emitted at the car were stretched by the car motion, to be
lambda = (v_sound + v_car)/440 [wave/s]

 

[lavafrog]

OK, I understand that my biker is moving towards the source, so the top should have a +. But then for the bottom, is it + because my source is moving away from my observer? (I know it's +, I just want to make sure that's the right reason.)

abercrombiems02--Thanks!