What Is the Wavelength of a Sound Wave in Steel?

[03sto]

Homework Statement

A sound wave is generated by a source of frequency 440hz is moving through 25 deg celcius air. The sound wave strikes a solid block of steel and propagates into the steel. What is the wavelength of the sound wave inside the steel. The density of steel is 7.85 g/cm^3 and the bulk modulus of steel is 1.6 x 10^11 n/m^2.

Homework Equations

331 + (.607 x temp in deg C)

The Attempt at a Solution

331 + (.607 x 25) = 346.175 air speed is about all i know for this problem... any help?

 

[anathema]

Hello,

Thank you for your post. To calculate the wavelength of the sound wave inside the steel, we can use the formula:

wavelength = speed of sound / frequency

Since we are given the frequency (440hz) and the temperature (25 degrees Celsius), we can use the formula you provided to calculate the speed of sound in air (346.175 m/s).

Next, we need to find the speed of sound in steel. This can be done using the formula:

speed of sound in steel = sqrt(bulk modulus / density)

Plugging in the values given (bulk modulus = 1.6 x 10^11 n/m^2 and density = 7.85 g/cm^3), we get a speed of sound in steel of approximately 5,039 m/s.

Now, we can use the formula for wavelength to calculate the wavelength of the sound wave in steel:

wavelength = 5,039 m/s / 440hz = 11.47 meters

Therefore, the wavelength of the sound wave inside the steel is 11.47 meters. I hope this helps. Let me know if you have any further questions or need clarification. Good luck with your studies!