Math Problem Statement
solve
Solution
Let's go through the questions one by one.
Question (a):
Comparing sounds A and B, how would they sound different?
- Sound A has fewer oscillations (waves) in the same amount of time, meaning lower frequency.
- Sound B has more oscillations, indicating higher frequency.
- A lower frequency sound (A) would have a lower pitch, while the higher frequency sound (B) would have a higher pitch.
Question (b):
Comparing sounds A and C, how would they sound different?
- Sound A has smoother, larger oscillations, meaning higher amplitude.
- Sound C has smaller, more compressed oscillations, meaning lower amplitude.
- A sound with a higher amplitude (A) would be louder, while a sound with a lower amplitude (C) would be quieter.
Question (c):
Which sound has the highest amplitude?
- From the waveforms, Sound A clearly has the largest oscillation peaks, meaning it has the highest amplitude.
Question (d):
Which sound has the highest frequency?
- Sound C has the most oscillations in the same time period, meaning it has the highest frequency.
Question (e):
The speed of sound is 330 m/s. If sound A has a frequency of 220 Hz, what is its wavelength?
The formula for the wavelength is: Substitute the given values: So, the wavelength of sound A is 1.5 meters.
Question (f):
What is the frequency of sound C?
Sound C has a higher frequency than sound A. From the waveform, you can see that Sound C has about three times the frequency of sound A. Since Sound A has a frequency of 220 Hz, Sound C would have approximately: So, the frequency of sound C is approximately 660 Hz.
Would you like further details on any specific part?
5 related questions:
- How does amplitude affect the loudness of sound?
- What is the relationship between frequency and pitch?
- How can the speed of sound change in different mediums?
- How would the waveform change if the sounds were mixed together?
- What is the typical range of human hearing in terms of frequency?
Tip: Remember that frequency determines the pitch of a sound, while amplitude determines its loudness.
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Math Problem Analysis
Mathematical Concepts
Wave Properties
Frequency
Amplitude
Wavelength
Formulas
Wavelength (λ) = Speed of Sound / Frequency
Frequency (f) = 1 / Time Period
Theorems
Relationship between frequency and pitch
Relationship between amplitude and loudness
Suitable Grade Level
Grades 9-11
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