At a concert, would the speed of sound be different for different frequencies? Why or why not?
No, sound speed is independent of frequency. It just IS. It depends only upon the temperature (not even the pressure) of the air it is going through. As for "why?", that requires a physical derivation, with thermodynamics considered. An adiabatic heating and rarefaction process is assumed when a sound wave passes by.
You can find a derivation of the speed of sound in gases at:
http://www.grc.nasa.gov/WWW/K-12/airplane/snddrv.html
but it requires math and physics that is above grade 11 level.
At 25°C, sound can travel 100 meters across a football field in 0.29 seconds. Determine the velocity of these sound waves.
Yes, the speed of sound would be different for different frequencies. This is because the speed of sound is influenced by the properties of the medium through which it travels, such as air or water.
To understand why the speed of sound varies with frequency, we need to look at how sound waves propagate. Sound waves are caused by the vibrations of particles in a medium. These vibrations generate wave-like motions that travel through the medium, carrying the sound information.
In simple terms, the speed of sound can be understood as the rate at which these vibrations propagate through the medium. However, the behavior of sound waves is influenced by various factors, including frequency.
One primary factor affecting the speed of sound is the compressibility of the medium. Sound travels by creating areas of compression and rarefaction in the medium, forming a pressure wave. The speed at which these compressions and rarefactions propagate can vary depending on the compressibility of the medium.
In the case of air, the medium we most commonly encounter for sound transmission, the compressibility is influenced by factors like temperature, humidity, and pressure. At a given temperature, air exhibits different compressibility characteristics for different sound frequencies.
Higher frequency sounds, such as those in the range of human speech or music, are typically associated with smaller wavelengths. These shorter wavelengths can be absorbed or scattered more easily by the air molecules, affecting the speed at which the sound wave travels. As a result, higher-frequency sounds may propagate slightly slower compared to lower-frequency sounds.
To determine the exact relationship between frequency and the speed of sound in a specific medium, like air, various parameters and equations are used. These include the properties of the medium itself, like density and temperature, as well as mathematical models describing wave propagation.
In conclusion, the speed of sound can vary for different frequencies because the behavior of sound waves is influenced by factors like compressibility and the physical properties of the medium through which they travel.