An informative illustration representing two different sound waves travelling through a hypothetical gas container. The first wave, Wave A, is depicted with a shorter wavelength of 1.2 meters. Contrastingly, Wave B is delineated with a longer wavelength of 3.6 meters. The representation should visually emphasize that Wave A has a relatively higher frequency compared to Wave B, thus visually providing the concept that the frequency of Wave B is one-third that of Wave A. There should not be any textual explanation or answers within the image.

Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The frequency of wave B must be __________ the frequency of wave A.

a. one-ninth
b. one-third
c. the same as
d. three times larger than

the answer is one third but i do not understand why some one please attempt to give some sort of explanation. Thank you!

Answer: C

The speed of a wave does not depend upon its wavelength, but rather upon the properties of the medium. The medium has not changed, so neither has the speed.

they both travel with the same speed. So, a longer wavelength means it oscillates more slowly.

Recall that

v = λf

3λ means f/3 to get the same v.

1.2 × 3 =3.6

So when cancelling 1.2 becomes 1 and 3.6 becomes 3.

Well, let me put on my clown nose and try to explain this with a little humor!

Imagine the two sound waves are running a race through the container of gas. Wave A, being the speed demon that it is, completes one full wavelength in 1.2 meters. Now, Wave B, being a bit more of a slowpoke, needs three times more space to finished a full wavelength, taking up 3.6 meters.

Now, let's think about frequency. Frequency is like the speed at which the waves run. If Wave A is zipping along, completing a full wavelength in 1.2 meters, and Wave B is taking its sweet time, needing 3.6 meters to do the same, logically we can conclude that Wave B's frequency must be slower, right?

Well, "one-third" is the answer because Wave B needs three times more space to complete a full wavelength than Wave A. So, Wave B is three times slower, or one-third of the frequency of Wave A.

I hope that explanation put a smile on your face!

To understand why the frequency of wave B is one-third the frequency of wave A, we can use the equation relating frequency, wavelength, and speed of a wave:

v = f * λ

where:
v = speed of the wave
f = frequency of the wave
λ = wavelength of the wave

Since both waves are traveling through the same container of gas, their speeds are the same. Therefore, we can equate the speeds of the two waves:

v (A) = v (B)

Using the equation, we can rearrange it to:

f (A) * λ (A) = f (B) * λ (B)

Given that the wavelength of wave A is 1.2 m and the wavelength of wave B is 3.6 m, substituting these values in the equation gives:

f (A) * 1.2 = f (B) * 3.6

To find the relationship between the frequencies, we need to cancel out the wavelength term. Since 1.2 is three times smaller than 3.6, we divide both sides of the equation by 1.2:

f (A) = f (B) * 3

This equation shows that the frequency of wave B must be one-third (1/3) the frequency of wave A, thus the answer is b. one-third.

To determine the relationship between the frequencies of wave A and wave B, we need to understand the fundamental relationship between the wavelength and frequency of a wave.

The relationship between wavelength (λ), frequency (f), and wave speed (v) is given by the equation:

v = λf

Here, v represents the speed at which the wave travels through a medium, λ represents the wavelength, and f represents the frequency of the wave.

In this case, since both waves are traveling through the same container of gas, they have the same wave speed. Therefore, we can equate the two expressions:

v₁ = v₂ (since both waves are in the same container of gas)

Using the equation v = λf, we can rewrite the above expression as:

λ₁f₁ = λ₂f₂

Given that the wavelength of wave A (λ₁) is 1.2 m, and the wavelength of wave B (λ₂) is 3.6 m, we can substitute these values into the equation:

1.2f₁ = 3.6f₂

To simplify the equation, we can divide both sides by 1.2:

f₁ = 3f₂

Now we can see that the frequency of wave A (f₁) is three times larger than the frequency of wave B (f₂). In other words, the frequency of wave B is one-third the frequency of wave A.

Therefore, the correct answer is b. one-third.

The answer is C

To know why
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