1. Air temperature in the Sahara Desert has been known to reach 56.0 °C (about 134 °F). You are there on a warm day and your thermometer reads 46° C. What is speed of sound given that the T°C temperature dependance of sound in air at 1 atm of pressure is v= (331m/s)/1+ ? 273°C V= m/s
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
![### Problem 1: Speed of Sound in Air
**Air temperature in the Sahara Desert has been known to reach 56.0°C (about 134°F). You are there on a warm day and your thermometer reads 46°C. What is the speed of sound given that the temperature dependence of sound in air at 1 atm of pressure is:**
\[ v = (331 \text{ m/s}) \sqrt{1 + \frac{T^\circ C}{273^\circ C}} \]
where:
- \( v \) is the speed of sound in meters per second (m/s),
- \( T^\circ C \) is the temperature in degrees Celsius (°C).
**Calculate the speed of sound:**
\[ v = \]
\[ \boxed{\sqrt{ }} \text{ m/s} \]
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**Explanation:**
This problem involves calculating the speed of sound in air based on the given temperature. The formula provided shows that the speed of sound \( v \) depends on the temperature \( T \) in degrees Celsius. To solve this, you need to plug the given temperature (46°C) into the formula.
1. Substitute \( T \) with 46°C in the equation.
2. Perform the calculation within the square root.
3. Multiply the result by 331 m/s to get the speed of sound.
This type of problem is useful for understanding how environmental factors like temperature can affect physical phenomena such as the propagation speed of sound waves.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff787f97c-9dc4-4f39-97ba-c4c8bbc1d69b%2F23266322-8ca2-47ba-a365-1cb4ac3c9760%2Fqpkvhz_processed.png&w=3840&q=75)
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