Question
Transverse waves with a frequency of 60 hertz propagate trough a medium. The maximum displacement of the medium from its resting position is 7 mm. The distance between five crests is 60 mm.
Questions
1. Draw a diagram and label it to show the waves.
2. Calculate the amplitude.
3. Calculate the period.
4. Calculate the wavelength.
5. Calculate the speed of the wave.
6. Calculate the distance a crest travels in 2 seconds.
Questions
1. Draw a diagram and label it to show the waves.
2. Calculate the amplitude.
3. Calculate the period.
4. Calculate the wavelength.
5. Calculate the speed of the wave.
6. Calculate the distance a crest travels in 2 seconds.
Answers
GPT-4o mini
Sure! Let's go through each of the questions one by one.
### 1. Diagram of the Wave
While I cannot draw, I can describe what to include in your diagram:
- Draw a horizontal line to represent the resting position of the medium.
- Draw a sine wave above and below this line to represent the transverse wave.
- Label the crests (the high points) and troughs (the low points).
- Mark the amplitude (the distance from the resting position to a crest or trough).
- Show the distance between several crests to emphasize the wavelength.
### 2. Calculate the Amplitude
The amplitude is given as the maximum displacement of the medium from its resting position, which is provided as 7 mm.
**Amplitude** = 7 mm
### 3. Calculate the Period
The period (T) is the reciprocal of the frequency (f). Given that the frequency is 60 Hz:
\[
T = \frac{1}{f} = \frac{1}{60 \, \text{Hz}} \approx 0.01667 \, \text{s} \, \text{(or 16.67 ms)}
\]
### 4. Calculate the Wavelength
The distance between five crests is given as 60 mm. To find the wavelength, we need to know that the distance between two consecutive crests is one wavelength (\(\lambda\)). Therefore:
\[
\text{Distance between 5 crests} = 4 \, \text{wavelengths}
\]
\[
\lambda = \frac{60 \, \text{mm}}{4} = 15 \, \text{mm}
\]
### 5. Calculate the Speed of the Wave
The speed of a wave (v) can be calculated using the formula:
\[
v = f \times \lambda
\]
Convert all measurements to meters for consistency.
- Frequency \(f = 60 \, \text{Hz}\)
- Wavelength \(\lambda = 15 \, \text{mm} = 0.015 \, \text{m}\)
Then:
\[
v = 60 \, \text{Hz} \times 0.015 \, \text{m} = 0.9 \, \text{m/s}
\]
### 6. Calculate the Distance a Crest Travels in 2 Seconds
To calculate the distance a crest travels in 2 seconds, use the speed of the wave:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = 0.9 \, \text{m/s} \times 2 \, \text{s} = 1.8 \, \text{m}
\]
### Summary of Answers:
1. (Diagram description provided above)
2. Amplitude = 7 mm
3. Period = 0.01667 s (or 16.67 ms)
4. Wavelength = 15 mm
5. Speed of the wave = 0.9 m/s
6. Distance a crest travels in 2 seconds = 1.8 m
Feel free to ask if you need further assistance!
### 1. Diagram of the Wave
While I cannot draw, I can describe what to include in your diagram:
- Draw a horizontal line to represent the resting position of the medium.
- Draw a sine wave above and below this line to represent the transverse wave.
- Label the crests (the high points) and troughs (the low points).
- Mark the amplitude (the distance from the resting position to a crest or trough).
- Show the distance between several crests to emphasize the wavelength.
### 2. Calculate the Amplitude
The amplitude is given as the maximum displacement of the medium from its resting position, which is provided as 7 mm.
**Amplitude** = 7 mm
### 3. Calculate the Period
The period (T) is the reciprocal of the frequency (f). Given that the frequency is 60 Hz:
\[
T = \frac{1}{f} = \frac{1}{60 \, \text{Hz}} \approx 0.01667 \, \text{s} \, \text{(or 16.67 ms)}
\]
### 4. Calculate the Wavelength
The distance between five crests is given as 60 mm. To find the wavelength, we need to know that the distance between two consecutive crests is one wavelength (\(\lambda\)). Therefore:
\[
\text{Distance between 5 crests} = 4 \, \text{wavelengths}
\]
\[
\lambda = \frac{60 \, \text{mm}}{4} = 15 \, \text{mm}
\]
### 5. Calculate the Speed of the Wave
The speed of a wave (v) can be calculated using the formula:
\[
v = f \times \lambda
\]
Convert all measurements to meters for consistency.
- Frequency \(f = 60 \, \text{Hz}\)
- Wavelength \(\lambda = 15 \, \text{mm} = 0.015 \, \text{m}\)
Then:
\[
v = 60 \, \text{Hz} \times 0.015 \, \text{m} = 0.9 \, \text{m/s}
\]
### 6. Calculate the Distance a Crest Travels in 2 Seconds
To calculate the distance a crest travels in 2 seconds, use the speed of the wave:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
\[
\text{Distance} = 0.9 \, \text{m/s} \times 2 \, \text{s} = 1.8 \, \text{m}
\]
### Summary of Answers:
1. (Diagram description provided above)
2. Amplitude = 7 mm
3. Period = 0.01667 s (or 16.67 ms)
4. Wavelength = 15 mm
5. Speed of the wave = 0.9 m/s
6. Distance a crest travels in 2 seconds = 1.8 m
Feel free to ask if you need further assistance!