Question
The table shows the speed of sound in various media.
Medium
Speed of
Sound (m/s)
Air 343
Glass 5,640
Steel 5,940
Water 1,433
If a sound wave transitions from one medium to another, which transition would result in a shortening of the wavelength of the sound wave?
(1 point)
Responses
steel to water
steel to water
air to steel
air to steel
water to glass
water to glass
air to glass
Medium
Speed of
Sound (m/s)
Air 343
Glass 5,640
Steel 5,940
Water 1,433
If a sound wave transitions from one medium to another, which transition would result in a shortening of the wavelength of the sound wave?
(1 point)
Responses
steel to water
steel to water
air to steel
air to steel
water to glass
water to glass
air to glass
Answers
GPT-4o mini
To determine which transition would result in a shortening of the wavelength of a sound wave, we need to consider the relationship between the speed of sound in a medium and the wavelength of the sound wave.
The speed of sound in a medium is given by the formula:
\[ v = f \lambda \]
where \( v \) is the speed of sound, \( f \) is the frequency of the sound wave, and \( \lambda \) is the wavelength. When sound transitions from one medium to another, the frequency remains constant (assuming no change in source), but the speed of sound can change, which will affect the wavelength.
The wavelength is given by:
\[ \lambda = \frac{v}{f} \]
If the speed of sound increases when transitioning from one medium to another, the wavelength will also increase, and if the speed of sound decreases, the wavelength will decrease.
Now let's analyze the transitions given:
1. **Steel to Water**:
- Speed of sound in steel: 5,940 m/s
- Speed of sound in water: 1,433 m/s
- This transition decreases the speed of sound, which will shorten the wavelength.
2. **Air to Steel**:
- Speed of sound in air: 343 m/s
- Speed of sound in steel: 5,940 m/s
- This transition increases the speed of sound, which will lengthen the wavelength.
3. **Water to Glass**:
- Speed of sound in water: 1,433 m/s
- Speed of sound in glass: 5,640 m/s
- This transition increases the speed of sound, which will lengthen the wavelength.
4. **Air to Glass**:
- Speed of sound in air: 343 m/s
- Speed of sound in glass: 5,640 m/s
- This transition increases the speed of sound, which will lengthen the wavelength.
Thus, the transition that results in a shortening of the wavelength of the sound wave is:
**Steel to Water**
The speed of sound in a medium is given by the formula:
\[ v = f \lambda \]
where \( v \) is the speed of sound, \( f \) is the frequency of the sound wave, and \( \lambda \) is the wavelength. When sound transitions from one medium to another, the frequency remains constant (assuming no change in source), but the speed of sound can change, which will affect the wavelength.
The wavelength is given by:
\[ \lambda = \frac{v}{f} \]
If the speed of sound increases when transitioning from one medium to another, the wavelength will also increase, and if the speed of sound decreases, the wavelength will decrease.
Now let's analyze the transitions given:
1. **Steel to Water**:
- Speed of sound in steel: 5,940 m/s
- Speed of sound in water: 1,433 m/s
- This transition decreases the speed of sound, which will shorten the wavelength.
2. **Air to Steel**:
- Speed of sound in air: 343 m/s
- Speed of sound in steel: 5,940 m/s
- This transition increases the speed of sound, which will lengthen the wavelength.
3. **Water to Glass**:
- Speed of sound in water: 1,433 m/s
- Speed of sound in glass: 5,640 m/s
- This transition increases the speed of sound, which will lengthen the wavelength.
4. **Air to Glass**:
- Speed of sound in air: 343 m/s
- Speed of sound in glass: 5,640 m/s
- This transition increases the speed of sound, which will lengthen the wavelength.
Thus, the transition that results in a shortening of the wavelength of the sound wave is:
**Steel to Water**