What is the wavelength of a sound wave?

In summary: That's why 261.6 hz is a good starting point, because it's close to the actual underwater frequency of the piano.
  • #1
huffy
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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.
 
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  • #2
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?
 
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  • #3
huffy said:
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 :)
 
  • #4
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?
 
  • #5
Right. You assumed the piano wire still makes that frequency under water. In reality the larger damping will shift the frequency a bit lower.
 

1. What is the definition of wavelength?

The wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, or have the same position in their respective cycles. This distance is typically measured from the peak of one wave to the peak of the next wave.

2. How is wavelength related to frequency?

Wavelength and frequency are inversely proportional to each other. This means that as the wavelength of a sound wave increases, the frequency decreases, and vice versa. This relationship is described by the formula: wavelength = speed of sound / frequency.

3. Can the wavelength of a sound wave change?

Yes, the wavelength of a sound wave can change depending on the medium it is traveling through. In general, sound travels faster in denser mediums, resulting in a shorter wavelength. Additionally, as the frequency of a sound wave increases, the wavelength decreases.

4. How is the wavelength of a sound wave measured?

The wavelength of a sound wave can be measured using a variety of techniques, such as using a ruler to measure the distance between two consecutive peaks or using specialized equipment like an oscilloscope to measure the distance between two points in the wave that are in phase.

5. Why is the wavelength of a sound wave important?

The wavelength of a sound wave is important because it determines the pitch of the sound. A shorter wavelength corresponds to a higher frequency and a higher-pitched sound, while a longer wavelength corresponds to a lower frequency and a lower-pitched sound. Wavelength also affects how sound behaves and travels through different mediums, such as air, water, or solid objects.

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