Question
The diagram illustrates the movement of a sound wave. The distance between points A and C is 9 meters (m), and initially, it takes the wave 3 seconds (s) to traverse this distance.
If the velocity of the wave remains constant but the pitch is tripled, what will be the wavelength of the sound wave?
(1 point)
Responses
3 meters
3 meters
18 meters
18 meters
9 meters
9 meters
6 meters
6 meters
Skip to navigation
If the velocity of the wave remains constant but the pitch is tripled, what will be the wavelength of the sound wave?
(1 point)
Responses
3 meters
3 meters
18 meters
18 meters
9 meters
9 meters
6 meters
6 meters
Skip to navigation
Answers
GPT-4o mini
To find the wavelength of the sound wave after tripling the pitch, we can use the relationship between speed (v), frequency (f), and wavelength (λ) given by the formula:
\[ v = f \times \lambda \]
First, we calculate the speed of the wave. The distance between points A and C is 9 meters, and it takes 3 seconds for the wave to travel that distance. Therefore, the speed of the wave (v) can be calculated as:
\[ v = \frac{\text{distance}}{\text{time}} = \frac{9 \text{ m}}{3 \text{ s}} = 3 \text{ m/s} \]
Next, we need to understand the relationship between pitch and frequency. The pitch of a sound wave is directly proportional to its frequency. If the pitch is tripled, the frequency also triples.
Let’s denote the original frequency as \( f \). After tripling, the new frequency \( f' \) becomes:
\[ f' = 3f \]
Now we can relate the original wavelength \( \lambda \) to the original frequency:
\[ v = f \times \lambda \]
\[ \lambda = \frac{v}{f} \]
Now for the new wavelength \( \lambda' \) using the new frequency \( f' \):
\[ \lambda' = \frac{v}{f'} = \frac{v}{3f} = \frac{\lambda}{3} \]
This means the new wavelength is one-third of the original wavelength.
Since we are not given the original wavelength \( \lambda \) directly but know that the wave travels 9 meters in total over the distance, we can assume that the wave was at least one full wavelength (or a multiple) in that distance. The problem doesn’t specify the initial wavelength directly, but in the same distance of 9 meters, since it already took and completed that journey, we can characterize the wavelength based on common wave characteristics.
However, since the available answer choices seem to imply a universally applicable change, we should focus on how wavelength changes with respect to pitch increased by a factor of 3.
Assuming the original wavelength could correspond to one full cycle over that distance or more, and our calculation shows that increasing frequency decreases wavelength, thus:
If the original wavelength was \( λ = 9 \) m, the new wavelength would be:
\[ \lambda' = \frac{9 \text{ m}}{3} = 3 \text{ m} \]
Based on that, the new wavelength when the pitch is tripled would indeed be:
**3 meters**.
\[ v = f \times \lambda \]
First, we calculate the speed of the wave. The distance between points A and C is 9 meters, and it takes 3 seconds for the wave to travel that distance. Therefore, the speed of the wave (v) can be calculated as:
\[ v = \frac{\text{distance}}{\text{time}} = \frac{9 \text{ m}}{3 \text{ s}} = 3 \text{ m/s} \]
Next, we need to understand the relationship between pitch and frequency. The pitch of a sound wave is directly proportional to its frequency. If the pitch is tripled, the frequency also triples.
Let’s denote the original frequency as \( f \). After tripling, the new frequency \( f' \) becomes:
\[ f' = 3f \]
Now we can relate the original wavelength \( \lambda \) to the original frequency:
\[ v = f \times \lambda \]
\[ \lambda = \frac{v}{f} \]
Now for the new wavelength \( \lambda' \) using the new frequency \( f' \):
\[ \lambda' = \frac{v}{f'} = \frac{v}{3f} = \frac{\lambda}{3} \]
This means the new wavelength is one-third of the original wavelength.
Since we are not given the original wavelength \( \lambda \) directly but know that the wave travels 9 meters in total over the distance, we can assume that the wave was at least one full wavelength (or a multiple) in that distance. The problem doesn’t specify the initial wavelength directly, but in the same distance of 9 meters, since it already took and completed that journey, we can characterize the wavelength based on common wave characteristics.
However, since the available answer choices seem to imply a universally applicable change, we should focus on how wavelength changes with respect to pitch increased by a factor of 3.
Assuming the original wavelength could correspond to one full cycle over that distance or more, and our calculation shows that increasing frequency decreases wavelength, thus:
If the original wavelength was \( λ = 9 \) m, the new wavelength would be:
\[ \lambda' = \frac{9 \text{ m}}{3} = 3 \text{ m} \]
Based on that, the new wavelength when the pitch is tripled would indeed be:
**3 meters**.