Not sure how to do this temp and freq problem

• xxiangel
In summary, the first problem can be solved using the relationship between the speed of sound and temperature in air, while the second problem can be solved using the formula for the fundamental frequency of a vibrating string and considering the effects of doubling the length and tension. Additional research and understanding of the concepts may be necessary to fully solve these problems.
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)

xxiangel said:
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.

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.

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.

1. What is the purpose of solving a temperature and frequency problem?

The purpose of solving a temperature and frequency problem is to better understand the relationship between these two variables and how they affect each other. This can be useful in many scientific fields, such as physics, chemistry, and meteorology.

2. How do I convert between different temperature and frequency units?

To convert between different units of temperature and frequency, you can use conversion formulas or conversion tables. It is important to make sure you are using the correct units and that your calculations are accurate.

3. Can you provide an example of a temperature and frequency problem?

One example of a temperature and frequency problem could be: "If the frequency of a sound wave is 500 Hz and the temperature is 25 degrees Celsius, what is the frequency of the sound wave when the temperature is increased to 30 degrees Celsius?"

4. How do temperature and frequency affect each other?

Temperature and frequency have a direct relationship, meaning that as one increases, the other also increases. This is known as a positive correlation. The specific relationship between the two variables can vary depending on the context, but they are always related.

5. What are some real-life applications of temperature and frequency problems?

Temperature and frequency problems have many real-life applications, such as in weather forecasting, designing musical instruments, and calibrating electronic devices. They are also important in understanding the behavior of gases and waves in various environments.

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