Not sure how to do this temp and freq problem

[xxiangel]

Can someone help me work these out!?

1) A sound travels 1,047 meters in 3 seconds in air. Find the air temperature. (Answer 31.3 degrees C??)

2) A guitar string plays a fundamental frequency of 400 Hz. Find the
frequency played if the string were twice as long and twice as tight. (Answer is 283 Hz)

 

[OlderDan]

Can someone help me work these out!?

1) A sound travels 1,047 meters in 3 seconds in air. Find the air temperature. (Answer 31.3 degrees C??)

2) A guitar string plays a fundamental frequency of 400 Hz. Find the
frequency played if the string were twice as long and twice as tight. (Answer is 283 Hz)

Do a bit of research in your textbook, or go to google and search on "speed of sound" and "vibrating string". Then give these a try on your own. If you still need some help, show us what you did.

 

[FredGarvin]

Here are some hints:

1) In a perfect gas there is a relationship between the speed of sound, c, and the ratio of specific heats, $$\gamma$$, gravity, $$g$$, ideal gas constant, $$R$$, and temperature, $$T$$. You have information to calculate c in your question.

2) There is an equation for calculating the fundamental frequency of a string. In that equation is the term for the length. What can you glean by doubling the length in that equation?

Let's see what you have done so far.

 

[Chi Meson]

THere are two formulas for determining the speed of sound in air as a function of temperature. Chances are you have not covered the "adiabatic bulk modulus" of air and so you will be using the simplified relationship based on 331 m/s at 0 degrees C. For every degree above zero, the speed of sound is 0.6m/s faster.

This relationship is what is most often used in high school physics. This works within the short range of temperatures of human habitat (approx -10 to +40 degrees C) but does not factor in the humidity of the air.

FOr the second question, look in your text for how the frequency is proportional to length and tension. As you look at the formula, notice what would happen if you put a "2" in front of both tension and length.