Question
A) If the wavelength of a wave in a particular medium is tripled, what will happen to the frequency
of the wave? (1 point)
It will become triple its original value.
It will become one third of its original value.
It will depend on the speed of the wave.
It will remain constant.
A) If the speed of sound in air is 340 m/s, approximately how long will it take the sound of a clap
of thunder to travel 2 kilometers? (1 point)
1.7 seconds
3.4 seconds
5.9 seconds
2.9 seconds
of the wave? (1 point)
It will become triple its original value.
It will become one third of its original value.
It will depend on the speed of the wave.
It will remain constant.
A) If the speed of sound in air is 340 m/s, approximately how long will it take the sound of a clap
of thunder to travel 2 kilometers? (1 point)
1.7 seconds
3.4 seconds
5.9 seconds
2.9 seconds
Answers
GPT-4o mini
**Part A:** The relationship between wavelength (\( \lambda \)), frequency (\( f \)), and wave speed (\( v \)) is given by the equation:
\[ v = f \cdot \lambda \]
If the wavelength is tripled (\( \lambda' = 3\lambda \)), to find the new frequency (\( f' \)), the equation becomes:
\[ v = f' \cdot (3\lambda) \]
Since the wave speed \( v \) remains constant in a given medium, we can set the equations equal to each other:
\[ f \cdot \lambda = f' \cdot (3\lambda) \]
Dividing both sides by \( \lambda \):
\[ f = 3f' \]
This implies that:
\[ f' = \frac{f}{3} \]
Therefore, if the wavelength of a wave is tripled, the frequency will become **one third of its original value**.
---
**Part B:** To calculate the time it takes for sound to travel 2 kilometers (2000 meters) at a speed of 340 m/s, you can use the formula:
\[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
Substituting the values:
\[ \text{time} = \frac{2000 \text{ m}}{340 \text{ m/s}} \]
Calculating that:
\[ \text{time} \approx 5.88 \text{ seconds} \]
Rounding it, the closest answer is **5.9 seconds**.
So the answers are:
- For part A: **It will become one third of its original value.**
- For part B: **5.9 seconds.**
\[ v = f \cdot \lambda \]
If the wavelength is tripled (\( \lambda' = 3\lambda \)), to find the new frequency (\( f' \)), the equation becomes:
\[ v = f' \cdot (3\lambda) \]
Since the wave speed \( v \) remains constant in a given medium, we can set the equations equal to each other:
\[ f \cdot \lambda = f' \cdot (3\lambda) \]
Dividing both sides by \( \lambda \):
\[ f = 3f' \]
This implies that:
\[ f' = \frac{f}{3} \]
Therefore, if the wavelength of a wave is tripled, the frequency will become **one third of its original value**.
---
**Part B:** To calculate the time it takes for sound to travel 2 kilometers (2000 meters) at a speed of 340 m/s, you can use the formula:
\[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
Substituting the values:
\[ \text{time} = \frac{2000 \text{ m}}{340 \text{ m/s}} \]
Calculating that:
\[ \text{time} \approx 5.88 \text{ seconds} \]
Rounding it, the closest answer is **5.9 seconds**.
So the answers are:
- For part A: **It will become one third of its original value.**
- For part B: **5.9 seconds.**