Frequency of Sound in Room-Temperature Air: 1 Meter Wavelength

[zachcumer]

Hello,
I have to answer this question in my Physics Class. "What frequency of sound produces a wavelength of 1 meter in room-temperature air? "

Could you help me?

Thanks

 

[ranger]

Can you tell us a formula that relates wavelength to its frequency?

Hint: it is an inverse relationship.

 

[zachcumer]

In the book, they say Frequency=1/period...

 

[zachcumer]

hello?

 

[ranger]

Indeed, f = 1/T. But that doesn't really help you here since we need wavelength. Theres also a reason why they mentioned the medium to be air at room temperature. This should tell you that the velocity depends on the medium through which the wave propagates. Now that I've told you that wavelength is somehow related to velocity of the wave and its frequency, can you piece it together to get a formula?

It should be somehow be obvious that the higher the frequency, the smaller the wavelength.

 

[zachcumer]

isnt the 1 meter the wavelength? confused?

 

[ranger]

Yes. But I find it much easier to reason out a formula which gives us wavelength in terms of velocity and frequency. Then you can solve the equation for frequency (but that's just me). Just a side note, the speed that sound propagates in air is around 345 m/s at room temp.

 

[zachcumer]

so its 345 times f= one meter...how do I find "f"?

 

[ranger]

Nice try. But remember that wavelength is inversely proportional to frequency.

 

[zachcumer]

oh its 344 thanks so so so so so so so much!

thanks again

 

[zachcumer]

What is the shortest wavelength you can hear?

 

[ranger]

Now that you have your formula relating frequency and wavelength. I'll tell you that the human ear has an audible range of about 20Hz - 20kHz. Its up to you express that as a wavelength.

 

[zachcumer]

So, 345 times 20 equals 6,900 centimeters...!>...!.

 

[zachcumer]

Nice try. But remember that wavelength is inversely proportional to frequency.

confused.

 

[ranger]

I was trying to get you to understand this:
http://en.wikipedia.org/wiki/Wavelength

 

[zachcumer]

I know I have to do something similar on this problem too: A bat flying in a cave emits a sound and receives its echo 1 s later. How far away is the cave wall?

 

[ranger]

The sound hits the wall in .5 secs and takes another .5 secs to return to the bat for a total time of 1 sec. What are the equations that relate velocity, time, and distance?

 

[zachcumer]

so its 345/2 or half of the speed of sound...
thanks

 

[ranger]

Looks good.