What is the wavelength of a sound wave?

[huffy]

Homework Statement

Alas, after a sybaritic festival, the cheap upright piano in your fraternity house is found upright at the bottom of the house swimming pool. You decide to play Handel's Water music but first test the sound of middle C (261.6 HZ). The speed of sound in water is 1.48x10^3 m/s. What is the wavelength of the sound wave corresponding to middle C in the pool? What is the assumptions are needed to make the determination?

v=1.48x10^3 m/s
f=261.6 Hz

Homework Equations

• λ=v/f
• v=(β/ρ)^1/2

The Attempt at a Solution

I just plugged it into the equation λ=v/f and got 5.66 m. Which I think is correct but I am not sure if I know all the assumptions or not. Thats where the next equation comes in, v=(β/ρ)^1/2, because I assume that to get the speed of sound in the water.

 

[Cutter Ketch]

Your first calculation is all you need. The speed of sound in water is given in the problem statement, so the second equation is not needed.

As to what assumptions, well you were given the speed of sound. If you know the frequency, then you have the wavelength. So any assumptions all come down to the frequency. What did you assume when you used that frequency in the calculation?

 

[Simon Bridge]

I just plugged it into the equation λ=v/f and got 5.66 m. Which I think is correct but I am not sure if I know all the assumptions or not. Thats where the next equation comes in, v=(β/ρ)^1/2, because I assume that to get the speed of sound in the water.

Start with the assumptions ... if you don't know what assumptions you are making, you how can you know if you have the equations that meet those assumptions. [edit] Cutter is nicer than me :)

 

[huffy]

So to use the information given that the frequency is indeed 261.6 hz, i have to assume that underwater the frequency won't change and that only the speed of the sound waves will change when calculating the wavelength underwater. Would you agree?

 

[Cutter Ketch]

Right. You assumed the piano wire still makes that frequency under water. In reality the larger damping will shift the frequency a bit lower.