Question
The speed of sound through a particular material is 4,700 m/s. If the frequency of a sound wave traveling through this material is tripled, what conclusion can be drawn?(1 point)
Responses
The wavelength of the wave will triple.
The wavelength of the wave will triple.
The wavelength of the wave will be one third of its original length..
The wavelength of the wave will be one third of its original length..
The speed of the sound wave will triple.
The speed of the sound wave will triple.
The speed of the sound wave will be one third of its original speed
A sound wave with a frequency of 440 Hz passes from one medium to another, correlating with an increase in the wavelength to twice as high. Which statement describes a cause of this correlation?(1 point)
Responses
The speed of the wave is doubled.
The speed of the wave is doubled.
The frequency of the wave is doubled.
The frequency of the wave is doubled.
The frequency of the wave is halved.
The frequency of the wave is halved.
The speed of the wave is halved.
As a sound wave travels deeper into the ocean, it encounters water that increases in density. What change is correlated with this move from shallow water to deep water?(1 point)
Responses
The wavelength of the wave increases.
The wavelength of the wave increases.
The frequency of the wave decreases.
The frequency of the wave decreases.
The speed of the wave decreases.
The speed of the wave decreases.
The speed of the wave remains constant.
Responses
The wavelength of the wave will triple.
The wavelength of the wave will triple.
The wavelength of the wave will be one third of its original length..
The wavelength of the wave will be one third of its original length..
The speed of the sound wave will triple.
The speed of the sound wave will triple.
The speed of the sound wave will be one third of its original speed
A sound wave with a frequency of 440 Hz passes from one medium to another, correlating with an increase in the wavelength to twice as high. Which statement describes a cause of this correlation?(1 point)
Responses
The speed of the wave is doubled.
The speed of the wave is doubled.
The frequency of the wave is doubled.
The frequency of the wave is doubled.
The frequency of the wave is halved.
The frequency of the wave is halved.
The speed of the wave is halved.
As a sound wave travels deeper into the ocean, it encounters water that increases in density. What change is correlated with this move from shallow water to deep water?(1 point)
Responses
The wavelength of the wave increases.
The wavelength of the wave increases.
The frequency of the wave decreases.
The frequency of the wave decreases.
The speed of the wave decreases.
The speed of the wave decreases.
The speed of the wave remains constant.
Answers
GPT-4o mini
Let's analyze each question separately.
1. **The speed of sound through a particular material is 4,700 m/s. If the frequency of a sound wave traveling through this material is tripled, what conclusion can be drawn?**
The relationship between speed (v), frequency (f), and wavelength (λ) of a wave is given by the equation:
\[ v = f \cdot \lambda \]
If the speed of sound in the material remains constant at 4,700 m/s and the frequency is tripled, we can express this as:
- Let the original frequency be \( f \).
- New frequency = \( 3f \).
We can set up the equation before and after the frequency change:
1. **Original:** \( v = f \cdot \lambda \)
2. **New:** \( v = 3f \cdot \lambda' \)
Since the speed of sound (v) is constant:
\[ f \cdot \lambda = 3f \cdot \lambda' \]
Solving for λ':
\[ \lambda = 3 \cdot \lambda' \]
\[ \lambda' = \frac{\lambda}{3} \]
This tells us that the new wavelength will be one third of its original length.
**Answer: The wavelength of the wave will be one third of its original length.**
---
2. **A sound wave with a frequency of 440 Hz passes from one medium to another, correlating with an increase in the wavelength to twice as high. Which statement describes a cause of this correlation?**
Using the wave equation \( v = f \cdot \lambda \), if the wavelength increases to twice its original length, the equation shows:
Let the original wavelength be \( \lambda \) and the new wavelength be \( 2\lambda \).
Because the speed of sound in different media can be different, let's assume the speed remains constant when it transitions if the medium doesn't change significantly. The new frequency \( f' \) can be calculated as:
1. Original: \( v = 440 \text{ Hz} \cdot \lambda \)
2. New: \( v = f' \cdot (2\lambda) \)
Since \( v \) is assumed to be constant between media, setting both expressions equal gives:
\[ 440 \cdot \lambda = f' \cdot (2\lambda) \]
\[ f' = \frac{440}{2} = 220 \text{ Hz} \]
Thus, the frequency is halved.
**Answer: The frequency of the wave is halved.**
---
3. **As a sound wave travels deeper into the ocean, it encounters water that increases in density. What change is correlated with this move from shallow water to deep water?**
As sound travels deeper into water, the propagation speed of sound typically increases due to factors like temperature and pressure, despite density increases. If the speed increases while the frequency remains constant, then the wavelength must also increase according to the wave equation \( v = f \cdot \lambda \).
Since we have relatively higher sound speed in deeper and denser water, we can infer that the wavelength increases because speed increases tends to dominate.
**Answer: The wavelength of the wave increases.**
1. **The speed of sound through a particular material is 4,700 m/s. If the frequency of a sound wave traveling through this material is tripled, what conclusion can be drawn?**
The relationship between speed (v), frequency (f), and wavelength (λ) of a wave is given by the equation:
\[ v = f \cdot \lambda \]
If the speed of sound in the material remains constant at 4,700 m/s and the frequency is tripled, we can express this as:
- Let the original frequency be \( f \).
- New frequency = \( 3f \).
We can set up the equation before and after the frequency change:
1. **Original:** \( v = f \cdot \lambda \)
2. **New:** \( v = 3f \cdot \lambda' \)
Since the speed of sound (v) is constant:
\[ f \cdot \lambda = 3f \cdot \lambda' \]
Solving for λ':
\[ \lambda = 3 \cdot \lambda' \]
\[ \lambda' = \frac{\lambda}{3} \]
This tells us that the new wavelength will be one third of its original length.
**Answer: The wavelength of the wave will be one third of its original length.**
---
2. **A sound wave with a frequency of 440 Hz passes from one medium to another, correlating with an increase in the wavelength to twice as high. Which statement describes a cause of this correlation?**
Using the wave equation \( v = f \cdot \lambda \), if the wavelength increases to twice its original length, the equation shows:
Let the original wavelength be \( \lambda \) and the new wavelength be \( 2\lambda \).
Because the speed of sound in different media can be different, let's assume the speed remains constant when it transitions if the medium doesn't change significantly. The new frequency \( f' \) can be calculated as:
1. Original: \( v = 440 \text{ Hz} \cdot \lambda \)
2. New: \( v = f' \cdot (2\lambda) \)
Since \( v \) is assumed to be constant between media, setting both expressions equal gives:
\[ 440 \cdot \lambda = f' \cdot (2\lambda) \]
\[ f' = \frac{440}{2} = 220 \text{ Hz} \]
Thus, the frequency is halved.
**Answer: The frequency of the wave is halved.**
---
3. **As a sound wave travels deeper into the ocean, it encounters water that increases in density. What change is correlated with this move from shallow water to deep water?**
As sound travels deeper into water, the propagation speed of sound typically increases due to factors like temperature and pressure, despite density increases. If the speed increases while the frequency remains constant, then the wavelength must also increase according to the wave equation \( v = f \cdot \lambda \).
Since we have relatively higher sound speed in deeper and denser water, we can infer that the wavelength increases because speed increases tends to dominate.
**Answer: The wavelength of the wave increases.**