Simple harmonics - sound waves

[Foxhound101]

Homework Statement

A 2.40 kHz sound wave is transmitted through an aluminum rod.

A) What is its wavelength in the aluminum?
B What is the sound wave's frequency when it passes into the air?
C) What is its wavelength in air?

The speed of sound in aluminum is 5100 m/s according to the book.

Homework Equations

Velocity=frequency*lambda

The Attempt at a Solution

So...This is what I was doing, which apparently is wrong.

Velocity=frequency*lambda

frequency=2.4 * 10^3 Hz
Velocity = 5100 meters/sec

5100m/s=(2.4 * 10^3)hz *lambda

lambda=2.125m

But apparently that isn't the answer for part A...So I must have done something wrong somewhere...

So...thank you in advance for any help.

 

[anathema]

Thank you for your question. I would be happy to assist you in finding the correct solution.

First, let's review the given information and equations. The speed of sound in a material can be calculated using the equation v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength.

For part A, we are given the frequency and the speed of sound in aluminum, and we need to find the wavelength. Therefore, we can rearrange the equation to solve for λ, which gives us λ = v/f.

Substituting the given values, we get λ = (5100 m/s) / (2.40 kHz) = 2.125 m. This is the correct answer for the wavelength in aluminum.

For part B, the sound wave passes from aluminum into air. The speed of sound in air is approximately 343 m/s. Using the same equation, we can calculate the frequency in air as f = v/λ = (343 m/s) / (2.125 m) = 161.41 Hz. This is the answer for part B.

Finally, for part C, we need to find the wavelength in air. Again, using the same equation, we get λ = v/f = (343 m/s) / (161.41 Hz) = 2.125 m. This is the same as the wavelength in aluminum, as the frequency does not change when the sound wave passes into a different medium.

I hope this helps clarify the solution for you. If you have any further questions, please do not hesitate to ask.

 

[baba89]

Your approach is correct, but you have used the wrong velocity value. The given velocity of 5100 m/s is for sound waves in aluminum, not for air. The velocity of sound in air is approximately 343 m/s. So, your calculation should be:

Velocity = frequency * lambda
343 m/s = (2.4 * 10^3) Hz * lambda
lambda = 0.143 m

Therefore, the wavelength of the sound wave in aluminum is 0.143 meters and in air is 2.125 meters.