Math Problem Statement

solve

A microphone is connected to an oscilloscope. When different sounds, A, B, and C, are made, these are the waveforms seen on the screen. Answer the following questions related to the sound waveforms.

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: Wavelength(λ)=Speed of SoundFrequency\text{Wavelength} (\lambda) = \frac{\text{Speed of Sound}}{\text{Frequency}} Substitute the given values: λ=330m/s220Hz=1.5m\lambda = \frac{330 \, \text{m/s}}{220 \, \text{Hz}} = 1.5 \, \text{m} 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: Frequency of C=220×3=660Hz\text{Frequency of C} = 220 \times 3 = 660 \, \text{Hz} So, the frequency of sound C is approximately 660 Hz.


Would you like further details on any specific part?

5 related questions:

  1. How does amplitude affect the loudness of sound?
  2. What is the relationship between frequency and pitch?
  3. How can the speed of sound change in different mediums?
  4. How would the waveform change if the sounds were mixed together?
  5. 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